Relevant bibliographies by topics / Application of the 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 'Application of the partial differential equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Application of the partial differential equations"

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Weerakoon, Sunethra. "Application of Sumudu transform to partial differential equations." International Journal of Mathematical Education in Science and Technology 25, no. 2 (April 1994): 277–83. http://dx.doi.org/10.1080/0020739940250214.

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代, 莹. "Application of Partial Differential Equations in Mathematical Models." Pure Mathematics 09, no. 06 (2019): 730–48. http://dx.doi.org/10.12677/pm.2019.96097.

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Stanković, B. "S-Bounded distributions, application to partial differential equations." Applicable Analysis 48, no. 1-4 (February 1993): 99–112. http://dx.doi.org/10.1080/00036819308840152.

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Bhalekar, Sachin, and Varsha Daftardar-Gejji. "New iterative method: Application to partial differential equations." Applied Mathematics and Computation 203, no. 2 (September 2008): 778–83. http://dx.doi.org/10.1016/j.amc.2008.05.071.

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Thornber, Mark, and G. L. Lamb. "Introductory Applications of Partial Differential Equations." Mathematical Gazette 83, no. 496 (March 1999): 184. http://dx.doi.org/10.2307/3618750.

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Morro, Angelo. "Introductory applications of partial differential equations." Meccanica 31, no. 6 (December 1996): 717–21. http://dx.doi.org/10.1007/bf00426978.

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Tahara, Hidetoshi. "Coupling of Two Partial Differential Equations and its Application." Publications of the Research Institute for Mathematical Sciences 43, no. 3 (2007): 535–83. http://dx.doi.org/10.2977/prims/1201012034.

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Fangliang, Dong. "Maximum Principle and Application of Parabolic Partial Differential Equations." IERI Procedia 3 (2012): 198–205. http://dx.doi.org/10.1016/j.ieri.2012.09.033.

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Manohar, R., and T. Y. Ngai. "Application of iteration functions to elliptic partial differential equations." Computers & Mathematics with Applications 16, no. 4 (1988): 279–85. http://dx.doi.org/10.1016/0898-1221(88)90144-7.

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Dattoli, G., B. Germano, M. R. Martinelli, and P. E. Ricci. "Monomiality and partial differential equations." Mathematical and Computer Modelling 50, no. 9-10 (November 2009): 1332–37. http://dx.doi.org/10.1016/j.mcm.2009.06.013.

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Dissertations / Theses on the topic "Application of the partial differential equations"

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McGee, Daniel Lee Jr. "Applications of neural networks to partial differential equations." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186885.

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Efforts to improve hyperthermia treatments of cancer have motivated this research. Three fundamental goals that have have been defined are the identification of tissue parameter values, the prediction of tissue temperature behavior, and the control of tissue temperature behavior during hyperthermia treatments. This dissertation consists of three independent studies plying neural networks to hyperthermia. These studies examine neural network based systems and how these systems apply to the identification, prediction, and control of tissue temperature behavior during a hyperthermia treatment. The first study examines the ability of neural networks to estimate the tissue perfusion values and the minimum temperature associated with numerically calculated steady state hyperthermia temperature fields. This study utilizes a limited number of measured temperatures within this field. We show that a hierarchical system of neural networks consisting of a first layer of pattern recognizing neural networks and a second layer of hypersurface reconstructing neural networks is capable of estimating these variables within a selected error tolerance. Additional results indicate that if the locations of the measured temperatures within the temperature field are selected effectively, the hierarchical system of neural networks can tolerate a moderate level of model mismatch. The second study examines the feasibility of using a system of neural networks to estimate the Laplacian values at the sensor locations in a tissue sample by using the measured temperature data. By combining these neural network Laplacian estimates with the measured data, numerical values for three different components (conduction, advection, and external power) can be obtained at the sensor locations. These thermal terms can then be used in a model of the tissue to predict future temperatures. Using only measured data collected early in the treatment, we show that recursive application of this estimation process can provide accurate predictions of the temperature behavior at the sensor locations of a tissue sample for the duration of a treatment. This system was also found to be robust with respect to the addition of white noise to both the sensor measurements and the amount of power delivered to the sensor locations. The final study explores the ability of a neural network based predictive system to formulate a predictive control strategy. We show that with certain restrictions on the power deposition patterns, desired temperature trajectories within the tissue model can be achieved with a neural network based predictive control system.
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Wu, Xiaoming. "Partial differential equations with applications to wave propagation." Thesis, University of Newcastle Upon Tyne, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239573.

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Seiler, Werner Markus. "Analysis and application of the formal theory of partial differential equations." Thesis, Lancaster University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.238979.

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Wright, S. J. "The application of transmission-line modelling implicit and hybrid algorithms to electromagnetic problems." Thesis, University of Nottingham, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384746.

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Mu, Tingshu. "Backward stochastic differential equations and applications : optimal switching, stochastic games, partial differential equations and mean-field." Thesis, Le Mans, 2020. http://www.theses.fr/2020LEMA1023.

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Cette thèse est relative aux Equations Différentielles Stochastique Rétrogrades (EDSRs) réfléchies avec deux obstacles et leurs applications aux jeux de switching de somme nulle, aux systèmes d’équations aux dérivées partielles, aux problèmes de mean-field. Il y a deux parties dans cette thèse. La première partie porte sur le switching optimal stochastique et est composée de deux travaux. Dans le premier travail, nous montrons l’existence de la solution d’un système d’EDSR réfléchies à obstacles bilatéraux interconnectés dans le cadre probabiliste général. Ce problème est lié à un jeu de switching de somme nulle. Ensuite nous abordons la question de l’unicité de la solution. Et enfin nous appliquons les résultats obtenus pour montrer que le système d’EDP associé à une unique solution au sens viscosité, sans la condition de monotonie habituelle. Dans le second travail, nous considérons aussi un système d’EDSRs réfléchies à obstacles bilatéraux interconnectés dans le cadre markovien. La différence avec le premier travail réside dans le fait que le switching ne s’opère pas de la même manière. Cette fois-ci quand le switching est opéré, le système est mis dans l’état suivant importe peu lequel des joueurs décide de switcher. Cette différence est fondamentale et complique singulièrement le problème de l’existence de la solution du système. Néanmoins, dans le cadre markovien nous montrons cette existence et donnons un résultat d’unicité en utilisant principalement la méthode de Perron. Ensuite, le lien avec un jeu de switching spécifique est établi dans deux cadres. Dans la seconde partie nous étudions les EDSR réfléchies unidimensionnelles à deux obstacles de type mean-field. Par la méthode du point fixe, nous montrons l’existence et l’unicité de la solution dans deux cadres, en fonction de l’intégrabilité des données
This thesis is related to Doubly Reflected Backward Stochastic Differential Equations (DRBSDEs) with two obstacles and their applications in zero-sum stochastic switching games, systems of partial differential equations, mean-field problems.There are two parts in this thesis. The first part deals with optimal stochastic switching and is composed of two works. In the first work we prove the existence of the solution of a system of DRBSDEs with bilateral interconnected obstacles in a probabilistic framework. This problem is related to a zero-sum switching game. Then we tackle the problem of the uniqueness of the solution. Finally, we apply the obtained results and prove that, without the usual monotonicity condition, the associated PDE system has a unique solution in viscosity sense. In the second work, we also consider a system of DRBSDEs with bilateral interconnected obstacles in the markovian framework. The difference between this work and the first one lies in the fact that switching does not work in the same way. In this second framework, when switching is operated, the system is put in the following state regardless of which player decides to switch. This difference is fundamental and largely complicates the problem of the existence of the solution of the system. Nevertheless, in the Markovian framework we show this existence and give a uniqueness result by the Perron’s method. Later on, two particular switching games are analyzed.In the second part we study a one-dimensional Reflected BSDE with two obstacles of mean-field type. By the fixed point method, we show the existence and uniqueness of the solution in connection with the integrality of the data
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Chen, Kewang. "Mathematical Analysis of Some Partial Differential Equations with Applications." ScholarWorks @ UVM, 2019. https://scholarworks.uvm.edu/graddis/1053.

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In the first part of this dissertation, we produce and study a generalized mathematical model of solid combustion. Our generalized model encompasses two special cases from the literature: a case of negligible heat diffusion in the product, for example, when the burnt product is a foam-like substance; and another case in which diffusivities in the reactant and product are assumed equal. In addition to that, our model pinpoints the dynamics in a range of settings, in which the diffusivity ratio between the burned and unburned materials varies between 0 and 1. The dynamics of temperature distribution and interfacial front propagation in this generalized solid combustion model are studied through both asymptotic and numerical analyses. For asymptotic analysis, we first analyze the linear instability of a basic solution to the generalized model. We then focus on the weakly nonlinear case where a small perturbation of a neutrally stable parameter is taken so that the linearized problem is marginally unstable. Multiple scale expansion method is used to obtain an asymptotic solution for large time by modulating the most linearly unstable mode. On the other hand, we integrate numerically the exact problem by the Crank-Nicolson method. Since the numerical solutions are very sensitive to the derivative interfacial jump condition, we integrate the partial differential equation to obtain an integral-differential equation as an alternative condition. The result system of nonlinear algebraic equations is then solved by the Newton’s method, taking advantage of the sparse structure of the Jacobian matrix. By a comparison of our asymptotic and numerical solutions, we show that our asymptotic solution captures the marginally unstable behaviors of the solution for a range of model parameters. Using the numerical solutions, we also delineate the role of the diffusivity ratio between the burned and unburned materials. We find that for a representative set of this parameter values, the solution is stabilized by increasing the temperature ratio between the temperature of the fresh mixture and the adiabatic temperature of the combustion products. This trend is quite linear when a parameter related to the activation energy is close to the stability threshold. Farther from this threshold, the behavior is more nonlinear as expected. Finally, for small values of the temperature ratio, we find that the solution is stabilized by increasing the diffusivity ratio. This stabilizing effect does not persist as the temperature ratio increases. Competing effects produce a “cross-over” phenomenon when the temperature ratio increases beyond about 0.2. In the second part, we study the existence and decay rate of a transmission problem for the plate vibration equation with a memory condition on one part of the boundary. From the physical point of view, the memory effect described by our integral boundary condition can be caused by the interaction of our domain with another viscoelastic element on one part of the boundary. In fact, the three different boundary conditions in our problem formulation imply that our domain is composed of two different materials with one condition imposed on the interface and two other conditions on the inner and outer boundaries, respectively. These transmission problems are interesting not only from the point of view of PDE general theory, but also due to their application in mechanics. For our mathematical analysis, we first prove the global existence of weak solution by using Faedo-Galerkin’s method and compactness arguments. Then, without imposing zero initial conditions on one part of the boundary, two explicit decay rate results are established under two different assumptions of the resolvent kernels. Both of these decay results allow a wider class of relaxation functions and initial data, and thus generalize some previous results existing in the literature.
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Pierson, Mark A. "Theory and Application of a Class of Abstract Differential-Algebraic Equations." Diss., Virginia Tech, 2005. http://hdl.handle.net/10919/27416.

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We first provide a detailed background of a geometric projection methodology developed by Professor Roswitha Marz at Humboldt University in Berlin for showing uniqueness and existence of solutions for ordinary differential-algebraic equations (DAEs). Because of the geometric and operator-theoretic aspects of this particular method, it can be extended to the case of infinite-dimensional abstract DAEs. For example, partial differential equations (PDEs) are often formulated as abstract Cauchy or evolution problems which we label abstract ordinary differential equations or AODE. Using this abstract formulation, existence and uniqueness of the Cauchy problem has been studied. Similarly, we look at an AODE system with operator constraint equations to formulate an abstract differential-algebraic equation or ADAE problem. Existence and uniqueness of solutions is shown under certain conditions on the operators for both index-1 and index-2 abstract DAEs. These existence and uniqueness results are then applied to some index-1 DAEs in the area of thermodynamic modeling of a chemical vapor deposition reactor and to a structural dynamics problem. The application for the structural dynamics problem, in particular, provides a detailed construction of the model and development of the DAE framework. Existence and uniqueness are primarily demonstrated using a semigroup approach. Finally, an exploration of some issues which arise from discretizing the abstract DAE are discussed.
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Guffey, Stephen. "Application of a Numerical Method and Optimal Control Theory to a Partial Differential Equation Model for a Bacterial Infection in a Chronic Wound." TopSCHOLAR®, 2015. https://digitalcommons.wku.edu/theses/1494.

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In this work, we study the application both of optimal control techniques and a numerical method to a system of partial differential equations arising from a problem in wound healing. Optimal control theory is a generalization of calculus of variations, as well as the method of Lagrange Multipliers. Both of these techniques have seen prevalent use in the modern theories of Physics, Economics, as well as in the study of Partial Differential Equations. The numerical method we consider is the method of lines, a prominent method for solving partial differential equations. This method uses finite difference schemes to discretize the spatial variable over an N-point mesh, thereby converting each partial differential equation into N ordinary differential equations. These equations can then be solved using numerical routines defined for ordinary differential equations.
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Coros, Corina Alexandra. "Analysis of partial differential equations with time-periodic forcing, applications to Navier-Stokes equations." Thesis, University of Ottawa (Canada), 2006. http://hdl.handle.net/10393/29346.

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Flows with time-periodic forcing can be found in various applications, such as the circulatory and respiratory systems, or industrial mixers. In this thesis, we address few questions in relation with the time-periodic forcing of flows and related partial differential equations (PDE), including the linear Advection-Diffusion equation. In Chapter 2, we first study linear PDE's with non-symmetric operators subject to time-periodic forcing. We prove that they have a unique time-periodic solution which is stable and attracts any initial solution if the bilinear form associated to the operator is coercive, and we obtain an error estimate for finite element method with a backward Euler time-stepping scheme. That general theory is applied to the Advection-Diffusion equation and the Stokes problem. The first equation has a non-symmetric operator, while the second has a symmetric operator but two unknowns, the velocity and pressure. To apply the general theory, we prove an error estimate for a Riesz projection operator, using a special Aubin-Nistche argument for the Advection-Diffusion equation with a tune-dependent advective velocity. A spectral analysis for the 1-D Advection-Diffusion equation, relevant parameters that control the speed of convergence of any initial solution to the time-periodic solution are identified. In Chapter 3, we extend a theorem of J.L. Lions about the existence of time-periodic solutions of Navier-Stokes equations under periodic distributed forcing with homogeneous Dirichlet boundary conditions to the case of non-homogeneous time-periodic Dirichlet boundary conditions. Our theorem predicts the existence of a time-periodic solution for Navier-Stokes equations subject to time-periodic forcing but the stability of these time-periodic solutions is not known. In Chapter 4, we investigate the stability of these time-periodic solutions, through numerical simulations with test cases in a 2-D time-periodic lid driven cavity and a 2-D constricted channel with a time-periodic inflow. From our numerical simulations, it seems that a bifurcation occurs in the range 3000--8000 in the periodically driven cavity, and the range 400--1200 in the periodically driven channel.
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Czapinski, Michal. "Solvers on Advanced Parallel Architectures with Application to Partial Differential Equations and Discrete Optimisation." Thesis, Cranfield University, 2014. http://dspace.lib.cranfield.ac.uk/handle/1826/9315.

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This thesis investigates techniques for the solution of partial differential equations (PDE) on advanced parallel architectures comprising central processing units (CPU) and graphics processing units (GPU). Many physical phenomena studied by scientists and engineers are modelled with PDEs, and these are often computationally expensive to solve. This is one of the main drivers of large-scale computing development. There are many well-established PDE solvers, however they are often inherently sequential. In consequence, there is a need to redesign the existing algorithms, and to develop new methods optimised for advanced parallel architectures. This task is challenging due to the need to identify and exploit opportunities for parallelism, and to deal with communication overheads. Moreover, a wide range of parallel platforms are available — interoperability issues arise if these are employed to work together. This thesis offers several contributions. First, performance characteristics of hybrid CPU-GPU platforms are analysed in detail in three case studies. Secondly, an optimised GPU implementation of the Preconditioned Conjugate Gradients (PCG) solver is presented. Thirdly, a multi-GPU iterative solver was developed — the Distributed Block Direct Solver (DBDS). Finally, and perhaps the most significant contribution, is the innovative streaming processing for FFT-based Poisson solvers. Each of these contributions offers significant insight into the application of advanced parallel systems in scientific computing. The techniques introduced in the case studies allow us to hide most of the communication overhead on hybrid CPU-GPU platforms. The proposed PCG implementation achieves 50–68% of the theoretical GPU peak performance, and it is more than 50% faster than the state-of-the-art solution (CUSP library). DBDS follows the Block Relaxation scheme to find the solution of linear systems on hybrid CPU-GPU platforms. The convergence of DBDS has been analysed and a procedure to compute a high-quality upper bound is derived. Thanks to the novel streaming processing technique, our FFT-based Poisson solvers are the first to handle problems larger than the GPU memory, and to enable multi- GPU processing with a linear speed-up. This is a significant improvement over the existing methods, which are designed to run on a single GPU, and are limited by the device memory size. Our algorithm needs only 6.9 seconds to solve a 2D Poisson problem with 2.4 billion variables (9 GB) on two Tesla C2050 GPUs (3 GB memory).
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Books on the topic "Application of the partial differential equations"

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Wazwaz, Abdul-Majid. Partial differential equations: Methods and applications. Lisse: Balkema, 2001.

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Partial differential equations: Methods and applications. Lisse [Netherlands]: A.A. Balkema, 2002.

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Rhee, Hyun-Ku. Theory and application of single equations. Englewood Cliffs, N.J: Prentice-Hall, 1986.

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Rhee, Hyun-Ku. Theory and application of single equations. Mineola, N.Y: Dover Publications, 2001.

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McOwen, Robert C. Partial differential equations: Methods and applications. 2nd ed. Upper Saddle, N.J: Prentice Hall, 2003.

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McOwen, Robert C. Partial differential equations: Methods and applications. Upper Saddle River, N.J: Prentice Hall, 1996.

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Nonlinear partial differential equations with applications. Boston, MA: Birkhauser Verlag, 2005.

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Analysis, partial differential equations and applications. Basel: Birkhäuser, 2009.

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Lamb, G. L. Introductory Applications of Partial Differential Equations. Hoboken, NJ, USA: John Wiley & Sons, Inc., 1995. http://dx.doi.org/10.1002/9781118032831.

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Guyenne, Philippe, David Nicholls, and Catherine Sulem, eds. Hamiltonian Partial Differential Equations and Applications. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-2950-4.

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Book chapters on the topic "Application of the partial differential equations"

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Lax, Peter D., and Maria Shea Terrell. "Partial differential equations." In Multivariable Calculus with Applications, 387–419. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-74073-7_9.

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Davies, B. "Application to Partial Differential Equations." In Integral Transforms and their Applications, 110–29. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4899-2691-3_8.

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Davies, B. "Partial Differential Equations." In Integral Transforms and their Applications, 47–58. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4899-2691-3_4.

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Denkowski, Zdzisław, Stanisław Migόrski, and Nikolas S. Papageorgiou. "Partial Differential Equations." In An Introduction to Nonlinear Analysis: Applications, 313–540. Boston, MA: Springer US, 2003. http://dx.doi.org/10.1007/978-1-4419-9156-0_3.

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Egorov, Yu V., and M. A. Shubin. "The Function P+λ for Polynomials of Second-degree and its Application in the Construction of Fundamental Solutions." In Partial Differential Equations II, 185–212. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57876-2_12.

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Kanwal, Ram P. "Applications to Partial Differential Equations." In Linear Integral Equations, 97–145. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-6012-1_6.

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Kanwal, Ram P. "Applications to Partial Differential Equations." In Linear Integral Equations, 97–145. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-0765-8_6.

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Logan, J. David. "Applications in the Life Sciences." In Applied Partial Differential Equations, 229–55. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12493-3_5.

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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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Holden, Helge, Bernt Øksendal, Jan Ubøe, and Tusheng Zhang. "Applications to Stochastic Ordinary Differential Equations." In Stochastic Partial Differential Equations, 115–57. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-89488-1_3.

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Conference papers on the topic "Application of the partial differential equations"

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Guo, Boling, and Dadi Yang. "Nonlinear Partial Differential Equations and Applications." In International Conference on Nonlinear Partial Differential Equations and Applications. WORLD SCIENTIFIC, 1998. http://dx.doi.org/10.1142/9789814527989.

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Cui, Xiaoke. "Application of partial differential equations in image processing." In International Conference on Education, Management and Computing Technology (ICEMCT-16). Paris, France: Atlantis Press, 2016. http://dx.doi.org/10.2991/icemct-16.2016.291.

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Hua, Chen, and Luigi Rodino. "Partial Differential Equations and Their Applications." In Proceedings of the Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789814527132.

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Chen, Baidi, and Fuyong An. "Application of Operator's Solution in Linear Partial Differential Equations." In 2013 Fifth International Conference on Computational and Information Sciences (ICCIS). IEEE, 2013. http://dx.doi.org/10.1109/iccis.2013.225.

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Potsepaev, R., and C. L. Farmer. "Application of Stochastic Partial Differential Equations to Reservoir Property Modelling." In 12th European Conference on the Mathematics of Oil Recovery. Netherlands: EAGE Publications BV, 2010. http://dx.doi.org/10.3997/2214-4609.20144964.

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Cheng, S. Y., Malcolm I. G. Bloor, A. Saia, and Michael J. Wilson. "Blending Between Quadric Surfaces Using Partial Differential Equations." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0031.

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Abstract The aim of this paper is to further illustrate the application of the PDE method in the field of blend generation, in particular the specification of the boundary conditions and their use in controlling the shape of the blend.
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Kansa, E. J. "Meshless solutions to multi-dimensional integral and partial differential equations." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 5th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS 13. AIP, 2013. http://dx.doi.org/10.1063/1.4827213.

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Dimiev, Stancho, Mihail Konstantinov, Vladimir Todorov, George Venkov, Ralitza Kovacheva, and Vesela Pasheva. "The coquaternion algebra and complex partial differential equations." In 35TH INTERNATIONAL CONFERENCE “APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS”: AMEE-2009. AIP, 2009. http://dx.doi.org/10.1063/1.3271612.

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Itu, Lucian Mihai, Constantin Suciu, Florin Moldoveanu, and Adrian Postelnicu. "GPU accelerated simulation of elliptic partial differential equations." In 2011 IEEE 6th International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS). IEEE, 2011. http://dx.doi.org/10.1109/idaacs.2011.6072748.

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Handibag, S. S., and B. D. Karande. "An application for nonlinear partial differential equations involving mixed partial derivatives by Laplace substitution method." In 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4904603.

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Reports on the topic "Application of the partial differential equations"

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Sharan, M., E. J. Kansa, and S. Gupta. Application of multiquadric method for numerical solution of elliptic partial differential equations. Office of Scientific and Technical Information (OSTI), January 1994. http://dx.doi.org/10.2172/10156506.

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Pulov,, Vladimir, and Ivan Uzunov. • Finding Lie Symmetries of Partial Differential Equations with MATHEMATICA®: Applications to Nonlinear Fiber Optics. GIQ, 2012. http://dx.doi.org/10.7546/giq-9-2008-280-291.

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Oliker, V. I., and P. Waltman. New Methods for Numerical Solution of One Class of Strongly Nonlinear Partial Differential Equations with Applications. Fort Belvoir, VA: Defense Technical Information Center, January 1986. http://dx.doi.org/10.21236/ada186166.

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Oliker, V. I., and P. Waltman. New Methods for Numerical Solution of One Class of Strongly Nonlinear Partial Differential Equations with Applications. Fort Belvoir, VA: Defense Technical Information Center, August 1987. http://dx.doi.org/10.21236/ada189945.

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Knightly, George H. An Analytical Study of Some Problems in Partial Differential Equations With Applications to Fluid Dynamics and Wave Propagation. Fort Belvoir, VA: Defense Technical Information Center, October 1992. http://dx.doi.org/10.21236/ada260351.

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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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