Relevant bibliographies by topics / Differential equations, Parabolic Reaction-diffusion equations Heat equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Conference papers

Academic literature on the topic 'Differential equations, Parabolic Reaction-diffusion equations Heat equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 February 2022

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Journal articles on the topic "Differential equations, Parabolic Reaction-diffusion equations Heat equation"

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Kravchenko, Vladislav V., Josafath A. Otero, and Sergii M. Torba. "Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable Coefficients." Advances in Mathematical Physics 2017 (2017): 1–5. http://dx.doi.org/10.1155/2017/2947275.

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A complete family of solutions for the one-dimensional reaction-diffusion equation, uxx(x,t)-q(x)u(x,t)=ut(x,t), with a coefficient q depending on x is constructed. The solutions represent the images of the heat polynomials under the action of a transmutation operator. Their use allows one to obtain an explicit solution of the noncharacteristic Cauchy problem with sufficiently regular Cauchy data as well as to solve numerically initial boundary value problems. In the paper, the Dirichlet boundary conditions are considered; however, the proposed method can be easily extended onto other standard
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ZAIN, F. MUHAMMAD, M. GARDA KHADAFI, and P. H. GUNAWAN. "ANALISIS KONVERGENSI METODE BEDA HINGGA DALAM MENGHAMPIRI PERSAMAAN DIFUSI." E-Jurnal Matematika 7, no. 1 (2018): 1. http://dx.doi.org/10.24843/mtk.2018.v07.i01.p176.

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The diffusion equation or known as heat equation is a parabolic and linear type of partial differential equation. One of the numerical method to approximate the solution of diffusion equations is Finite Difference Method (FDM). In this study, the analysis of numerical convergence of FDM to the solution of diffusion equation is discussed. The analytical solution of diffusion equation is given by the separation of variables approach. Here, the result show the convergence of rate the numerical method is approximately approach 2. This result is in a good agreement with the spatial error from Taylo
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Kazakov, Alexander. "Solutions to Nonlinear Evolutionary Parabolic Equations of the Diffusion Wave Type." Symmetry 13, no. 5 (2021): 871. http://dx.doi.org/10.3390/sym13050871.

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The article deals with nonlinear second-order evolutionary partial differential equations (PDEs) of the parabolic type with a reasonably general form. We consider the case of PDE degeneration when the unknown function vanishes. Similar equations in various forms arise in continuum mechanics to describe some diffusion and filtration processes as well as to model heat propagation in the case when the properties of the process depend significantly on the unknown function (concentration, temperature, etc.). One of the exciting and meaningful classes of solutions to these equations is diffusion (he
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Miller, Andrew, Jan Petrich, and Shashi Phoha. "Advanced Image Analysis for Learning Underlying Partial Differential Equations for Anomaly Identification." Journal of Imaging Science and Technology 64, no. 2 (2020): 20510–1. http://dx.doi.org/10.2352/j.imagingsci.technol.2020.64.2.020510.

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Abstract In this article, the authors adapt and utilize data-driven advanced image processing and machine learning techniques to identify the underlying dynamics and the model parameters for dynamic processes driven by partial differential equations (PDEs). Potential applications include non-destructive inspection for material crack detection using thermal imaging as well as real-time anomaly detection for process monitoring of three-dimensional printing applications. A neural network (NN) architecture is established that offers sufficient flexibility for spatial and temporal derivatives to ca
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Nakshatrala, K. B., H. Nagarajan, and M. Shabouei. "A Numerical Methodology for Enforcing Maximum Principles and the Non-Negative Constraint for Transient Diffusion Equations." Communications in Computational Physics 19, no. 1 (2016): 53–93. http://dx.doi.org/10.4208/cicp.180615.280815a.

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AbstractTransient diffusion equations arise in many branches of engineering and applied sciences (e.g., heat transfer and mass transfer), and are parabolic partial differential equations. It is well-known that these equations satisfy important mathematical properties like maximum principles and the non-negative constraint, which have implications in mathematical modeling. However, existing numerical formulations for these types of equations do not, in general, satisfy maximum principles and the non-negative constraint. In this paper, we present a methodology for enforcing maximum principles an
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Cruz-Quintero, Eduardo, and Francisco Jurado. "Boundary Control for a Certain Class of Reaction-Advection-Diffusion System." Mathematics 8, no. 11 (2020): 1854. http://dx.doi.org/10.3390/math8111854.

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There are physical phenomena, involving diffusion and structural vibrations, modeled by partial differential equations (PDEs) whose solution reflects their spatial distribution. Systems whose dynamics evolve on an infinite-dimensional Hilbert space, i.e., infinite-dimensional systems, are modeled by PDEs. The aim when designing a controller for infinite-dimensional systems is similar to that for finite-dimensional systems, i.e., the control system must be stable. Another common goal is to design the controller in such a way that the response of the system does not be affected by external distu
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Okino, T., T. Shimozaki, R. Fukuda, and Hiroki Cho. "Analytical Solutions of the Boltzmann Transformation Equation." Defect and Diffusion Forum 322 (March 2012): 11–31. http://dx.doi.org/10.4028/www.scientific.net/ddf.322.11.

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The so-called continuity equation derived by Fick is one of the most fundamental and extremely important equations in physics and/or in materials science. As is well known, this partial differential equation is also called the diffusion equation or the heat conduction equation and is applicable to physical phenomena of the conservation system. Incorporating the parabolic law relevant to a random movement into it, Boltzmann obtained the ordinary differential equation (B-equation). Matano then applied the B-equation to the analysis of the nonlinear problem for the interdiffusion experiment. The
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Kazakov, A. L., and P. A. Kuznetsov. "Analytical Diffusion Wave-type Solutions to a Nonlinear Parabolic System with Cylindrical and Spherical Symmetry." Bulletin of Irkutsk State University. Series Mathematics 37 (2021): 31–46. http://dx.doi.org/10.26516/1997-7670.2021.37.31.

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The paper deals with a second-order nonlinear parabolic system that describes heat and mass transfer in a binary liquid mixture. The nature of nonlinearity is such that the system has a trivial solution where its parabolic type degenerates. This circumstance allows us to consider a class of solutions having the form of diffusion waves propagating over a zero background with a finite velocity. We focus on two spatially symmetric cases when one of the two independent variables is time, and the second is the distance to a certain point or line. The existence and uniqueness theorem of the diffusio
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Promislow, Keith, John Stockie, and Brian Wetton. "A sharp interface reduction for multiphase transport in a porous fuel cell electrode." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2067 (2006): 789–816. http://dx.doi.org/10.1098/rspa.2005.1577.

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The gas diffusion layer in the electrode of a proton exchange membrane fuel cell is a highly porous material which acts to distribute reactant gases uniformly to the active catalyst sites. We analyse the conservation laws governing the multiphase flow of liquid, gas and heat within the electrode. The model is comprised of five nonlinear-degenerate parabolic differential equations strongly coupled through liquid–gas phase change. We identify a scaling regime in which the model reduces to a free boundary problem for a moving two-phase interface. On each side of the moving boundary the nonlinear
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Kudrna, Vladimír. "Certain problems with the application of stochastic diffusion processes for description of chemical engineering phenomena; Kolmogorov and classic diffusion equations." Collection of Czechoslovak Chemical Communications 53, no. 6 (1988): 1181–97. http://dx.doi.org/10.1135/cccc19881181.

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The paper presents alternative forms of partial differential equations of the parabolic type used in chemical engineering for description of heat and mass transfer. It points at the substantial difference between the classic form of the equations, following from the differential balances of mass and enthalpy, and the form following from the concept of stochastic motion of particles of mass or energy component. Examples are presented of the processes that may be described by the latter method. The paper also reviews the cases when the two approaches become identical.
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Dissertations / Theses on the topic "Differential equations, Parabolic Reaction-diffusion equations Heat equation"

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Knaub, Karl R. "On the asymptotic behavior of internal layer solutions of advection-diffusion-reaction equations /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/6772.

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Larsson, Stig. "On reaction-diffusion equation and their approximation by finite element methods /." Göteborg : Chalmers tekniska högskola, Dept. of Mathematics, 1985. http://bibpurl.oclc.org/web/32831.

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Sathinarain, Melisha. "Numerical investigation of the parabolic mixed-derivative diffusion equation via alternating direction implicit methods." Thesis, 2013. http://hdl.handle.net/10539/13016.

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A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment of the requirements for the degree of Master of Science, May 14, 2013.<br>In this dissertation, we investigate the parabolic mixed derivative diffusion equation modeling the viscous and viscoelastic effects in a non-Newtonian viscoelastic fluid. The model is analytically considered using Fourier and Laplace transformations. The main focus of the dissertation, however, is the implementation of the Peaceman-Rachford Alternating Direction Implicit method. The one-dimensional parabolic mixed der
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Books on the topic "Differential equations, Parabolic Reaction-diffusion equations Heat equation"

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Maximum Principles On Riemannian Manifolds And Applications (Memoirs of the American Mathematical Society). American Mathematical Society, 2005.

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Conference papers on the topic "Differential equations, Parabolic Reaction-diffusion equations Heat equation"

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Elperin, Tov, Andrew Fominykh, and Zakhar Orenbakh. "Mass Transfer During Fluid Sphere Dissolution in an Alternating Electric Field." In ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ht-fed2004-56270.

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In this study we considered mass transfer in a binary system comprising a stationary fluid dielectric sphere embedded into an immiscible dielectric liquid under the influence of an alternating electric field. Fluid sphere is assumed to be solvent-saturated so that an internal resistance to mass transfer can be neglected. Mass flux is directed from a fluid sphere to a host medium, and the applied electric field causes a creeping flow around the sphere. Droplet deformation under the influence of the electric field is neglected. The problem is solved in the approximations of a thin concentration
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Burbelko, Andriy A., Daniel Gurgul, Edward Fras´, and Edward Guzik. "Multiscale Modeling of Ductile Iron Solidification With Continuous Nucleation by a Cellular Automaton." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28764.

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The solidification of metals and alloys is a typical example of multiphysics and multiscale engineering systems. The phenomenon of different time and spatial scales should be taken into consideration in the modeling of a microstructure formation: heat diffusion, the components diffusion in the liquid and solid phases, the thermodynamics of phase transformation under a condition of inhomogeneous chemical composition of growing and vanishing phases, phase interface kinetics, and grains nucleation. The results of a two-dimensional modeling of the microstructure formation in a ductile cast iron ar
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