Relevant bibliographies by topics / Diffusion partial differential equations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Diffusion partial differential equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Diffusion partial differential equations"

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Benedetti, I., N. V. Loi, L. Malaguti, and V. Taddei. "Nonlocal diffusion second order partial differential equations." Journal of Differential Equations 262, no. 3 (February 2017): 1499–523. http://dx.doi.org/10.1016/j.jde.2016.10.019.

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Bertrand, Nicolas, Jocelyn Sabatier, Olivier Briat, and Jean-Michel Vinassa. "An Implementation Solution for Fractional Partial Differential Equations." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/795651.

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The link between fractional differentiation and diffusion equation is used in this paper to propose a solution for the implementation of fractional diffusion equations. These equations permit us to take into account species anomalous diffusion at electrochemical interfaces, thus permitting an accurate modeling of batteries, ultracapacitors, and fuel cells. However, fractional diffusion equations are not addressed in most commercial software dedicated to partial differential equations simulation. The proposed solution is evaluated in an example.
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Bonito, Andrea, Albert Cohen, Ronald DeVore, Guergana Petrova, and Gerrit Welper. "Diffusion Coefficients Estimation for Elliptic Partial Differential Equations." SIAM Journal on Mathematical Analysis 49, no. 2 (January 2017): 1570–92. http://dx.doi.org/10.1137/16m1094476.

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Goyal, Kavita, and Mani Mehra. "Fast diffusion wavelet method for partial differential equations." Applied Mathematical Modelling 40, no. 7-8 (April 2016): 5000–5025. http://dx.doi.org/10.1016/j.apm.2015.10.054.

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Carvalho, Alexandre N., and Luiz Augusto F. Oliveira. "Delay-partial differential equations with some large diffusion." Nonlinear Analysis: Theory, Methods & Applications 22, no. 9 (May 1994): 1057–95. http://dx.doi.org/10.1016/0362-546x(94)90228-3.

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Aziz, Imran, and Imran Khan. "Numerical Solution of Diffusion and Reaction–Diffusion Partial Integro-Differential Equations." International Journal of Computational Methods 15, no. 06 (September 2018): 1850047. http://dx.doi.org/10.1142/s0219876218500470.

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In this paper, a collocation method based on Haar wavelet is developed for numerical solution of diffusion and reaction–diffusion partial integro-differential equations. The equations are parabolic partial integro-differential equations and we consider both one-dimensional and two-dimensional cases. Such equations have applications in several practical problems including population dynamics. An important advantage of the proposed method is that it can be applied to both linear as well as nonlinear problems with slide modification. The proposed numerical method is validated by applying it to various benchmark problems from the existing literature. The numerical results confirm the accuracy, efficiency and robustness of the proposed method.
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Lin, Xiaodong, Joseph W. H. So, and Jianhong Wu. "Centre manifolds for partial differential equations with delays." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 122, no. 3-4 (1992): 237–54. http://dx.doi.org/10.1017/s0308210500021090.

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SynopsisA centre manifold theory for reaction-diffusion equations with temporal delays is developed. Besides an existence proof, we also show that the equation on the centre manifold is a coupled system of scalar ordinary differential equations of higher order. As an illustration, this reduction procedure is applied to the Hutchinson equation with diffusion.
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Zhao, Weng Cang, and Fan Wang. "Face Image Denoising Method Based on Fourth-Order Partial Differential Equations." Advanced Engineering Forum 6-7 (September 2012): 700–703. http://dx.doi.org/10.4028/www.scientific.net/aef.6-7.700.

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In order to improve the effect of face image denoising, this paper put forward several face image denoising methods based on partial differential equations, including P-M non-linear diffusion equations and fourth-order partial differential equations. We use those two methods by establishing non-linear diffusion equations and fourth-order anisotropic diffusion partial differential equation. The P-M non-linear diffusion denoising method can remove noise in intra-regions sufficiently but noise at edges can not be eliminated successfully and line-like structures can not be held very well.While the fourth-order partial differential equations denoising can retain the local detail characteristics of the original face image. Finally, through the experimental results we can see the effect of the fourth-order partial differential equations denoising is better, which makes the later face image processing more accurate and promotes the development of face image processing.
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Aljedhi, Reem Abdullah, and Adem Kılıçman. "Fractional Partial Differential Equations Associated with Lêvy Stable Process." Mathematics 8, no. 4 (April 2, 2020): 508. http://dx.doi.org/10.3390/math8040508.

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In this study, we first present a time-fractional L e ^ vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L e ^ vy-time fractional diffusion equation of European-style options. Further, we introduce a more general model based on the L e ^ vy-time fractional diffusion equation and review some recent findings associated with risk-neutral free European option pricing.
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Abdel-Gawad, H. I. "Solution of a class of partial differential equations. Some diffusion equations." Mathematical Methods in the Applied Sciences 12, no. 3 (March 1990): 221–28. http://dx.doi.org/10.1002/mma.1670120305.

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Dissertations / Theses on the topic "Diffusion partial differential equations"

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Trojan, Alice von. "Finite difference methods for advection and diffusion." Title page, abstract and contents only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phv948.pdf.

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Includes bibliographical references (leaves 158-163). Concerns the development of high-order finite-difference methods on a uniform rectangular grid for advection and diffuse problems with smooth variable coefficients. This technique has been successfully applied to variable-coefficient advection and diffusion problems. Demonstrates that the new schemes may readily be incorporated into multi-dimensional problems by using locally one-dimensional techniques, or that they may be used in process splitting algorithms to solve complicatef time-dependent partial differential equations.
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Chow, Tanya L. M., of Western Sydney Macarthur University, and Faculty of Business and Technology. "Systems of partial differential equations and group methods." THESIS_FBT_XXX_Chow_T.xml, 1996. http://handle.uws.edu.au:8081/1959.7/43.

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This thesis is concerned with the derivation of similarity solutions for one-dimensional coupled systems of reaction - diffusion equations, a semi-linear system and a one-dimensional tripled system. The first area of research in this thesis involves a coupled system of diffusion equations for the existence of two distinct families of diffusion paths. Constructing one-parameter transformation groups preserving the invariance of this system of equations enables similarity solutions for this coupled system to be derived via the classical and non-classical procedures. This system of equation is the uncoupled in the hope of recovering further similarity solutions for the system. Once again, one-parameter groups leaving the uncoupled system invariant are obtained, enabling similarity solutions for the system to be elicited. A one-dimensional pattern formation in a model of burning forms the next component of this thesis. The primary focus of this area is the determination of similarity solutions for this reaction - diffusion system by means of one-parameter transformation group methods. Consequently, similarity solutions which are a generalisation of the solutions of the one-dimensional steady equations derived by Forbes are deduced. Attention in this thesis is then directed toward a semi-linear coupled system representing a predator - prey relationship. Two approaches to solving this system are made using the classical procedure, leading to one-parameter transformation groups which are instrumental in elicting the general similarity solution for this system. A triple system of equations representing a one-dimensional case of diffusion in the presence of three diffusion paths constitutes the next theme of this thesis. In association with the classical and non-classical procedures, the derivation of one-parameter transformation groups leaving this system invariant enables similarity solutions for this system to be deduced. The final strand of this thesis involves a one- dimensional case of the general linear system of coupled diffusion equations with cross-effects for which one-parameter transformation group methods are once more employed. The one-parameter groups constructed for this system prove instrumental in enabling the attainment of similarity solutions for this system to be accomplished
Faculty of Business and Technology
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Garvie, Marcus Roland. "Analysis of a reaction-diffusion system of λ-w type." Thesis, Durham University, 2003. http://etheses.dur.ac.uk/4105/.

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The author studies two coupled reaction-diffusion equations of 'λ-w' type, on an open, bounded, convex domain Ω C R(^d) (d ≤ 3), with a boundary of class C², and homogeneous Neumann boundary conditions. The equations are close to a supercritical Hopf bifurcation in the reaction kinetics, and are model equations for oscillatory reaction-diffusion equations. Global existence, uniqueness and continuous dependence on initial data of strong and weak solutions are proved using the classical Faedo-Galerkin method of Lions and compactness arguments. The work provides a complete case study for the application of this method to systems of nonlinear reaction-diffusion equations. The author also undertook the numerical analysis of the reaction-diffusion system. Results are presented for a fully-practical piecewise linear finite element method by mimicking results in the continuous case. Semi-discrete and fully-discrete error estimates are proved after establishing a priori bounds for various norms of the approximate solutions. Finally, the theoretical results are illustrated and verified via the numerical simulation of periodic plane waves in one space dimension, and preliminary results representing target patterns and spiral solutions presented in two space dimensions.
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Mbroh, Nana Adjoah. "On the method of lines for singularly perturbed partial differential equations." University of the Western Cape, 2017. http://hdl.handle.net/11394/5679.

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Magister Scientiae - MSc
Many chemical and physical problems are mathematically described by partial differential equations (PDEs). These PDEs are often highly nonlinear and therefore have no closed form solutions. Thus, it is necessary to recourse to numerical approaches to determine suitable approximations to the solution of such equations. For solutions possessing sharp spatial transitions (such as boundary or interior layers), standard numerical methods have shown limitations as they fail to capture large gradients. The method of lines (MOL) is one of the numerical methods used to solve PDEs. It proceeds by the discretization of all but one dimension leading to systems of ordinary di erential equations. In the case of time-dependent PDEs, the MOL consists of discretizing the spatial derivatives only leaving the time variable continuous. The process results in a system to which a numerical method for initial value problems can be applied. In this project we consider various types of singularly perturbed time-dependent PDEs. For each type, using the MOL, the spatial dimensions will be discretized in many different ways following fitted numerical approaches. Each discretisation will be analysed for stability and convergence. Extensive experiments will be conducted to confirm the analyses.
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Palitta, Davide. "Preconditioning strategies for the numerical solution of convection-diffusion partial differential equations." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7464/.

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Il trattamento numerico dell'equazione di convezione-diffusione con le relative condizioni al bordo, comporta la risoluzione di sistemi lineari algebrici di grandi dimensioni in cui la matrice dei coefficienti è non simmetrica. Risolutori iterativi basati sul sottospazio di Krylov sono ampiamente utilizzati per questi sistemi lineari la cui risoluzione risulta particolarmente impegnativa nel caso di convezione dominante. In questa tesi vengono analizzate alcune strategie di precondizionamento, atte ad accelerare la convergenza di questi metodi iterativi. Vengono confrontati sperimentalmente precondizionatori molto noti come ILU e iterazioni di tipo inner-outer flessibile. Nel caso in cui i coefficienti del termine di convezione siano a variabili separabili, proponiamo una nuova strategia di precondizionamento basata sull'approssimazione, mediante equazione matriciale, dell'operatore differenziale di convezione-diffusione. L'azione di questo nuovo precondizionatore sfrutta in modo opportuno recenti risolutori efficienti per equazioni matriciali lineari. Vengono riportati numerosi esperimenti numerici per studiare la dipendenza della performance dei diversi risolutori dalla scelta del termine di convezione, e dai parametri di discretizzazione.
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Mateos, González Álvaro. "Asymptotic Analysis of Partial Differential Equations Arising in Biological Processes of Anomalous Diffusion." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEN069/document.

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Cette thèse est consacrée à l'analyse asymptotique d'équations aux dérivées partielles issues de modèles de déplacement sous-diffusif en biologie cellulaire. Notre motivation biologique est fondée sur les nombreuses observation récentes de protéinescytoplasmiques dont le déplacement aléatoire dévié de la diffusion Fickienne normale. Dans la première partie, nous étudions la décroissance auto-similaire de la solution d'une équation de renouvellement à queue lourde vers un état stationnaire. Les idéesmises en jeu sont inspirées de méthodes d'entropie relative. Nos principaux apports sont la preuve d'un taux de décroissance en norme L1 vers la loi de l'arc-sinus et l'introduction d'une fonction pivot spécifique dans une méthode d'entropie relative.La seconde partie porte sur la limite hyperbolique d'une équation de renouvellement structurée en âge et à sauts en espace. Nous y prouvons un résultat de « stabilité » : les solutions des problèmes rééchelonnés à ε > 0 convergent lorsque ε --> 0 vers la solution de viscosité de l'équation de Hamilton-Jacobi limite des problèmes à ε > 0. Les outilsmis en jeu proviennent de la théorie des équations de Hamilton-Jacobi.Ce travail présente trois idées intéressantes. La première est celle de prouver le résultat de convergence sur la condition de bord du problème plutôt que d'utiliser des fonctions test perturbées. La deuxième consiste en l'introduction de termes correcteurslogarithmiques en temps dans des estimations a priori ne découlant pas directementdu principe du maximum. Cela est dû à la non-existence d'un équilibre du problèmehomogène en espace. La troisième est une estimation précise de la décroissance de l'influence de la condition initiale sur le terme de renouvellement. Elle correspond à une estimation fine d'une version non-locale de la dérivée temporelle de la solution. Au cours de cette thèse, des simulations numériques de type Monte Carlo, schémas volumes finis, Lax-Friedrichs et Weighted Essentially Non Oscillating ont été réalisées
This thesis is devoted to the asymptotic analysis of partial differential equations modelling subdiffusive random motion in cell biology. The biological motivation for this work is the numerous recent observations of cytoplasmic proteins whose random motion deviates from normal Fickian diffusion. In the first part, we study the self-similar decay towards a steady state of the solution of a heavy-tailed renewal equation. The ideas therein are inspired from relative entropy methods. Our main contributions are the proof of an L1 decay rate towards the arc-sine distribution and the introduction of a specific pivot function in a relative entropy method.The second part treats the hyperbolic limit of an age-structured space-jump renewal equation. We prove a "stability" result: the solutions of the rescaled problems at ε > 0 converge as ε --> 0 towards the viscosity solution of the limiting Hamilton-Jacobi equation of the ε > 0 problems. The main mathematical tools used come from the theory of Hamilton-Jacobi equations. This work presents three interesting ideas. The first is that of proving the convergence result on the boundary condition of the studied problem rather than using perturbed test functions. The second consists in the introduction of time-logarithmic correction termsin a priori estimates that do not follow directly from the maximum principle. That is due to the non-existence of a suitable equilibrium for the space-homogenous problem. The third is a precise estimate of the decay of the inuence of the initial condition on the renewal term. This is tantamount to a refined estimate of a non-local version of the time derivative of the solution. Throughout this thesis, we have performed numerical simulations of different types: Monte Carlo, finite volume schemes, Lax-Friedrichs schemes and Weighted Essentially Non Oscillating schemes
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Manay, Siddharth. "Applications of anti-geometric diffusion of computer vision : thresholding, segmentation, and distance functions." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/33626.

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Perella, Andrew James. "A class of Petrov-Galerkin finite element methods for the numerical solution of the stationary convection-diffusion equation." Thesis, Durham University, 1996. http://etheses.dur.ac.uk/5381/.

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A class of Petrov-Galerkin finite element methods is proposed for the numerical solution of the n dimensional stationary convection-diffusion equation. After an initial review of the literature we describe this class of methods and present both asymptotic and nonasymptotic error analyses. Links are made with the classical Galerkin finite element method and the cell vertex finite volume method. We then present numerical results obtained for a selection of these methods applied to some standard test problems. We also describe extensions of these methods which enable us to solve accurately for derivative values of the solution.
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Lin, Xuelei. "Preconditioning techniques for all-at-once linear systems arising from advection diffusion equations." HKBU Institutional Repository, 2020. https://repository.hkbu.edu.hk/etd_oa/803.

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In this thesis, we mainly study preconditioning techniques for all-at-once linear systems arising from discretization of three types of time-dependent advection-diffusion equation: linear diffusion equation, constant-coefficients advection-diffusion equation, time-fractional sub-diffusion equation. The proposed preconditioners are used with Krylov subspace solvers. The preconditioner developed for linear diffusion equation is based on -circulant ap- proximation of temporal discretization. Diagonalizability, clustering of spectrum and identity-plus-low-rank decomposition are derived for the preconditioned matrix. We also show that generalized minimal residual (GMRES) solver for the preconditioned system has a linear convergence rate independent of matrix-size. The preconditioner for constant-coefficients advection-diffusion equation is based on approximating the discretization of advection term with a matrix diagonalizable by sine transform. Eigenvalues of the preconditioned matrix are proven to be lower and upper bounded by positive constants independent of discretization parameters. Moreover, as the preconditioner is based on spatial approximation, it is also applicable to steady-state problem. We show that GMRES for the preconditioned steady-state problem has a linear convergence rate independent of matrix size. The preconditioner for time-fractional sub-diffusion equation is based on approximat- ing the discretization of diffusion term with a matrix diagonalizable by sine transform. We show that the condition number of the preconditioned matrix is bounded by a constant independent of discretization parameters so that the normalized conjugate gradient (NCG) solver for the preconditioned system has a linear convergence rate independent of discretization parameters and matrix size. Fast implementations based on fast Fourier transform (FFT), fast sine transform (FST) or multigrid approximation are proposed for the developed preconditioners. Numerical results are reported to show the performance of the developed preconditioners
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Shen, Wensheng. "Computer Simulation and Modeling of Physical and Biological Processes using Partial Differential Equations." UKnowledge, 2007. http://uknowledge.uky.edu/gradschool_diss/501.

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Scientific research in areas of physics, chemistry, and biology traditionally depends purely on experimental and theoretical methods. Recently numerical simulation is emerging as the third way of science discovery beyond the experimental and theoretical approaches. This work describes some general procedures in numerical computation, and presents several applications of numerical modeling in bioheat transfer and biomechanics, jet diffusion flame, and bio-molecular interactions of proteins in blood circulation. A three-dimensional (3D) multilayer model based on the skin physical structure is developed to investigate the transient thermal response of human skin subject to external heating. The temperature distribution of the skin is modeled by a bioheat transfer equation. Different from existing models, the current model includes water evaporation and diffusion, where the rate of water evaporation is determined based on the theory of laminar boundary layer. The time-dependent equation is discretized using the Crank-Nicolson scheme. The large sparse linear system resulted from discretizing the governing partial differential equation is solved by GMRES solver. The jet diffusion flame is simulated by fluid flow and chemical reaction. The second-order backward Euler scheme is applied for the time dependent Navier-Stokes equation. Central difference is used for diffusion terms to achieve better accuracy, and a monotonicity-preserving upwind difference is used for convective ones. The coupled nonlinear system is solved via the damped Newton's method. The Newton Jacobian matrix is formed numerically, and resulting linear system is ill-conditioned and is solved by Bi-CGSTAB with the Gauss-Seidel preconditioner. A novel convection-diffusion-reaction model is introduced to simulate fibroblast growth factor (FGF-2) binding to cell surface molecules of receptor and heparan sulfate proteoglycan and MAP kinase signaling under flow condition. The model includes three parts: the flow of media using compressible Navier-Stokes equation, the transport of FGF-2 using convection-diffusion transport equation, and the local binding and signaling by chemical kinetics. The whole model consists of a set of coupled nonlinear partial differential equations (PDEs) and a set of coupled nonlinear ordinary differential equations (ODEs). To solve the time-dependent PDE system we use second order implicit Euler method by finite volume discretization. The ODE system is stiff and is solved by an ODE solver VODE using backward differencing formulation (BDF). Findings from this study have implications with regard to regulation of heparin-binding growth factors in circulation.
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Books on the topic "Diffusion partial differential equations"

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Taira, Kazuaki. Diffusion processes and partial differential equations. Boston: Academic Press, 1988.

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Lamb, G. L. Introductory applicationsof partial differential equations: With emphasis on wave propagation and diffusion. New York: John Wiley & Sons, 1995.

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Introductory applications of partial differential equations with emphasis on wave propagation and diffusion. New York: Wiley, 1995.

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Richard, Ghez, ed. Diffusion phenomena: Cases and studies. 2nd ed. New York: Kluwer Academic/Plenum Publishers, 2001.

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Selvadurai, A. P. S. Partial Differential Equations in Mechanics 1: Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000.

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Dynkin, E. B. Superdiffusions and positive solutions of nonlinear partial differential equations. Providence, R.I: American Mathematical Society, 2004.

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Jan, Verwer, ed. Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003.

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Jüngel, Ansgar. Entropy Methods for Diffusive Partial Differential Equations. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-34219-1.

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Wang, Haiyan, Feng Wang, and Kuai Xu. Modeling Information Diffusion in Online Social Networks with Partial Differential Equations. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38852-2.

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Favini, Angelo. Degenerate Nonlinear Diffusion Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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Book chapters on the topic "Diffusion partial differential equations"

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Kevorkian, J. "The Diffusion Equation." In Partial Differential Equations, 1–47. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-9022-0_1.

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Epstein, Marcelo. "The Diffusion Equation." In Partial Differential Equations, 209–38. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55212-5_10.

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Stroock, Daniel W., and S. R. Srinivasa Varadhan. "Parabolic Partial Differential Equations." In Multidimensional Diffusion Processes, 65–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-28999-2_4.

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Jost, Jürgen. "Reaction–Diffusion Equations and Systems." In Partial Differential Equations, 127–48. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4809-9_6.

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Volpert, Vitaly. "Nonlocal Reaction-diffusion Equations." In Elliptic Partial Differential Equations, 521–626. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0813-2_9.

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Kuznetsov, Yuri A. "Mixed Finite Element Methods on Polyhedral Meshes for Diffusion Equations." In Partial Differential Equations, 27–41. Dordrecht: Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-8758-5_2.

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Volpert, Vitaly. "Reaction-diffusion Problems with Convection." In Elliptic Partial Differential Equations, 391–451. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0813-2_6.

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Volpert, Vitaly. "Reaction-diffusion Processes, Models and Applications." In Elliptic Partial Differential Equations, 3–78. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0813-2_1.

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Volpert, Vitaly. "Reaction-diffusion Problems in Bounded Domains." In Elliptic Partial Differential Equations, 123–200. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0813-2_3.

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Vázquez, Juan Luis. "Nonlinear Diffusion with Fractional Laplacian Operators." In Nonlinear Partial Differential Equations, 271–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25361-4_15.

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Conference papers on the topic "Diffusion partial differential equations"

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Chen, Yujuan, and Mingxin Wang. "BLOW-UP PROBLEMS FOR PARTIAL DIFFERENTIAL EQUATIONS AND SYSTEMS OF PARABOLIC TYPE." In The International Conference on Reaction-Diffusion System and Viscosity Solutions. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812834744_0012.

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Li, Lanlan, and Jinsong Wu. "Partial differential equation diffusion in complex domain." In 2016 International Conference on Advances in Computing, Communications and Informatics (ICACCI). IEEE, 2016. http://dx.doi.org/10.1109/icacci.2016.7732050.

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Waldron, Will. "A method for solving 2D nonlinear partial differential equations exemplified by the heat-diffusion equation." In Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXX, edited by Keith A. Krapels and Gerald C. Holst. SPIE, 2019. http://dx.doi.org/10.1117/12.2513623.

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Surana, K. S., and M. A. Bona. "Computations of Higher Class Solutions of Partial Differential Equations." In ASME 2001 Engineering Technology Conference on Energy. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/etce2001-17142.

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Abstract This paper presents a new computational strategy, computational framework and mathematical framework for numerical computations of higher class solutions of differential and partial differential equations. The approach presented here utilizes ‘strong forms’ of the governing differential equations (GDE’s) and least squares approach in constructing the integral form. The conventional, or currently used, approaches seek the convergence of a solution in a fixed (order) space by h, p or hp-adaptive processes. The fundamental point of departure in the proposed approach is that we seek convergence of the computed solution by changing the orders of the spaces of the basis functions. With this approach convergence rates much higher than those from h,p–processes are achievable and the progressively computed solutions converge to the ‘strong’ i.e. ‘theoretical’ solutions of the GDE’s. Many other benefits of this approach are discussed and demonstrated. Stationary and time-dependant convection-diffusion and Burgers equations are used as model problems.
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Chaturvedi, Nalin A., Jake F. Christensen, Reinhardt Klein, and Aleksandar Kojic. "Approximations for Partial Differential Equations Appearing in Li-Ion Battery Models." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-4072.

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Li-ion based batteries are believed to be the most promising battery system for HEV/PHEV/EV applications due to their high energy density, lack of hysteresis and low self-discharge currents. However, designing a battery, along with its Battery Management System (BMS), that can guarantee safe and reliable operation, is a challenge since aging and other mechanisms involving optimal charge and discharge of the battery are not sufficiently well understood. In a previous article [1], we presented a model that has been studied in [2]–[5] to understand the operation of a Li-ion battery. In this article, we continue our work and present an approximation technique that can be applied to a generic battery model. These approximation method is based on projecting solutions to a Hilbert subspace formed by taking the span of an countably infinite set of basis functions. In this article, we apply this method to the key diffusion equation in the battery model, thus providing a fast approximation for the single particle model (SPM) for both variable and constant diffusion case.
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Belfkih, S., P. Montesinos, and R. Beuscart. "Edge detection using on partial differential equation and anisotropic diffusion." In Seventh International Symposium on Signal Processing and Its Applications, 2003. Proceedings. IEEE, 2003. http://dx.doi.org/10.1109/isspa.2003.1224763.

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Dudret, Stephane, Fouad Ammouri, and Pierre Rouchon. "Input/output transfer models of binary distillation columns derived from convection-diffusion partial differential equations." In 2013 IEEE 52nd Annual Conference on Decision and Control (CDC). IEEE, 2013. http://dx.doi.org/10.1109/cdc.2013.6760859.

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Wiedemann, Thomas, Christoph Manss, Dmitriy Shutin, Achim J. Lilienthal, Valentina Karolj, and Alberto Viseras. "Probabilistic modeling of gas diffusion with partial differential equations for multi-robot exploration and gas source localization." In 2017 European Conference on Mobile Robots (ECMR). IEEE, 2017. http://dx.doi.org/10.1109/ecmr.2017.8098707.

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Rand, Richard H., William I. Newman, Bruce C. Denardo, and Alice L. Newman. "Dynamics of a Nonlinear Parametrically-Excited Partial Differential Equation." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0247.

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Abstract We investigate a nonlinear Mathieu equation with diffusion and damping, using both perturbation theory and numerical integration. The perturbation results predict that for parameters which lie near the 2 : 1 resonance tongue of instability corresponding to a mode shape cos nx the resonant mode achieves a stable periodic motion, while all the other modes are predicted to decay to zero. By numerically integrating the p.d.e. as well as a 3-mode o.d.e. truncation, the predictions of perturbation theory are shown to represent an oversimplified picture of the dynamics. In particular it is shown that steady states exist which involve many modes. The dependence of steady state behavior on parameter values and initial conditions is investigated numerically.
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Chen, Y. G., W. G. Price, and P. Temarel. "An Improved Anti-Diffusive VOF Method to Predict Two-Fluid Free Surface Flows." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-50220.

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This investigation continues the development of an anti-diffusive volume of fluid method [1] by improving accuracy through the addition of an artificial diffusion term, with a negative diffusion coefficient, to the original advection equation describing the evolution of the fluid volume fraction. The advection and diffusion processes are split into a set of two partial differential equations (PDEs). The improved anti-diffusive Volume of Fluid (VOF) method is coupled with a two-fluid flow solver to predict free surface flows and illustrated by examples given in two-dimensional flows. The first numerical example is a solitary wave travelling in a tank. The second example is a plunging wave generated by flow over a submerged obstacle of prescribed shape on a horizontal floor. The computational results are validated against available experimental data.
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Reports on the topic "Diffusion partial differential equations"

1

Dresner, L. Asymptotic behavior of solutions of diffusion-like partial differential equations invariant to a family of affine groups. Office of Scientific and Technical Information (OSTI), July 1990. http://dx.doi.org/10.2172/6697591.

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Shearer, Michael. Systems of Hyperbolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, December 1994. http://dx.doi.org/10.21236/ada290287.

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Seidman, Thomas I. Nonlinear Systems of Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1989. http://dx.doi.org/10.21236/ada217581.

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Dalang, Robert C., and N. Frangos. Stochastic Hyperbolic and Parabolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, July 1994. http://dx.doi.org/10.21236/ada290372.

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Hale, Jack, Constantine M. Dafermos, John Mallet-Paret, Panagiotis E. Souganidis, and Walter Strauss. Dynamical Systems and Nonlinear Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, January 1989. http://dx.doi.org/10.21236/ada255356.

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Arnold, Douglas, N, ed. Compatible Spatial Discretizations for Partial Differential Equations. Office of Scientific and Technical Information (OSTI), November 2004. http://dx.doi.org/10.2172/834807.

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Hyman, J. M., M. Shashkov, M. Staley, S. Kerr, S. Steinberg, and J. Castillo. Mimetic difference approximations of partial differential equations. Office of Scientific and Technical Information (OSTI), August 1997. http://dx.doi.org/10.2172/518902.

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Shearer, Michael. Systems of Nonlinear Hyperbolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, December 1997. http://dx.doi.org/10.21236/ada344449.

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Dafermos, Constantine M., John Mallet-Paret, Panagiotis E. Souganidis, and Walter Strauss. Dynamical Systems and Nonlinear Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1993. http://dx.doi.org/10.21236/ada271514.

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Sharp, D. H., S. Habib, and M. B. Mineev. Numerical Methods for Stochastic Partial Differential Equations. Office of Scientific and Technical Information (OSTI), July 1999. http://dx.doi.org/10.2172/759177.

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