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Relevant bibliographies by topics / Diffusion-reaction equation

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Academic literature on the topic 'Diffusion-reaction equation'

Author: Grafiati

Published: 4 May 2024

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Journal articles on the topic "Diffusion-reaction equation"

1

Seki, Kazuhiko, Mariusz Wojcik, and M. Tachiya. "Fractional reaction-diffusion equation." Journal of Chemical Physics 119, no. 4 (July 22, 2003): 2165–70. http://dx.doi.org/10.1063/1.1587126.

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Angstmann, Christopher N., and Bruce I. Henry. "Time Fractional Fisher–KPP and Fitzhugh–Nagumo Equations." Entropy 22, no. 9 (September 16, 2020): 1035. http://dx.doi.org/10.3390/e22091035.

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A standard reaction–diffusion equation consists of two additive terms, a diffusion term and a reaction rate term. The latter term is obtained directly from a reaction rate equation which is itself derived from known reaction kinetics, together with modelling assumptions such as the law of mass action for well-mixed systems. In formulating a reaction–subdiffusion equation, it is not sufficient to know the reaction rate equation. It is also necessary to know details of the reaction kinetics, even in well-mixed systems where reactions are not diffusion limited. This is because, at a fundamental level, birth and death processes need to be dealt with differently in subdiffusive environments. While there has been some discussion of this in the published literature, few examples have been provided, and there are still very many papers being published with Caputo fractional time derivatives simply replacing first order time derivatives in reaction–diffusion equations. In this paper, we formulate clear examples of reaction–subdiffusion systems, based on; equal birth and death rate dynamics, Fisher–Kolmogorov, Petrovsky and Piskunov (Fisher–KPP) equation dynamics, and Fitzhugh–Nagumo equation dynamics. These examples illustrate how to incorporate considerations of reaction kinetics into fractional reaction–diffusion equations. We also show how the dynamics of a system with birth rates and death rates cancelling, in an otherwise subdiffusive environment, are governed by a mass-conserving tempered time fractional diffusion equation that is subdiffusive for short times but standard diffusion for long times.

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Ipsen, M., F. Hynne, and P. G. Sørensen. "Amplitude Equations and Chemical Reaction–Diffusion Systems." International Journal of Bifurcation and Chaos 07, no. 07 (July 1997): 1539–54. http://dx.doi.org/10.1142/s0218127497001217.

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The paper discusses the use of amplitude equations to describe the spatio-temporal dynamics of a chemical reaction–diffusion system based on an Oregonator model of the Belousov–Zhabotinsky reaction. Sufficiently close to a supercritical Hopf bifurcation the reaction–diffusion equation can be approximated by a complex Ginzburg–Landau equation with parameters determined by the original equation at the point of operation considered. We illustrate the validity of this reduction by comparing numerical spiral wave solutions to the Oregonator reaction–diffusion equation with the corresponding solutions to the complex Ginzburg–Landau equation at finite distances from the bifurcation point. We also compare the solutions at a bifurcation point where the systems develop spatio-temporal chaos. We show that the complex Ginzburg–Landau equation represents the dynamical behavior of the reaction–diffusion equation remarkably well, sufficiently far from the bifurcation point for experimental applications to be feasible.

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Păuna, Alina-Maria. "The auxiliary equation approach for solving reaction-diffusion equations." Journal of Physics: Conference Series 2719, no. 1 (February 1, 2024): 012002. http://dx.doi.org/10.1088/1742-6596/2719/1/012002.

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Abstract The paper concerns the auxiliary equation method and proposes an approach for finding the most general nonlinear term that can generalize a nonlinear differential equation, so that it keeps solutions expressed in terms of the same auxiliary equation. More precisely we will consider the second order reaction-diffusion equations and we will find the most general nolinear term of this type of equations, for which the solutions can be expressed in terms of the Riccati equation. The procedure is exemplified on Fitzhugh-Nagumo, Dodd-Bullough-Mikhailov, and Klein-Gordon models, seen as reaction-diffusion equations.

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Wang, Yulan, Xiaojun Song, and Chao Ye. "Fujita Exponent for a Nonlinear Degenerate Parabolic Equation with Localized Source." Advances in Mathematical Physics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/301747.

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This paper is devoted to understand the blow-up properties of reaction-diffusion equations which combine a localized reaction term with nonlinear diffusion. In particular, we study the critical exponent of ap-Laplacian equation with a localized reaction. We obtain the Fujita exponentqcof the equation.

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Wu, G., Eric Wai Ming Lee, and Gao Li. "Numerical solutions of the reaction-diffusion equation." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 2 (March 2, 2015): 265–71. http://dx.doi.org/10.1108/hff-04-2014-0113.

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Purpose – The purpose of this paper is to introduce variational iteration method (VIM) to construct equivalent integral equations for initial-boundary value problems of nonlinear partial differential equations. The Lagrange multipliers become the integral kernels. Design/methodology/approach – Using the discrete numerical integral formula, the general way is given to solve the famous reaction-diffusion equation numerically. Findings – With the given explicit solution, the results show the conveniences of the general numerical schemes and numerical simulation of the reaction-diffusion is finally presented in the cases of various coefficients. Originality/value – The method avoids the treatment of the time derivative as that in the classical finite difference method and the VIM is introduced to construct equivalent integral equations for initial-boundary value problems of nonlinear partial differential equations.

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Agom, E. U., F. O. Ogunfiditimi, E. V. Bassey, and C. Igiri. "REACTION-DIFFUSION FISHER’S EQUATIONS VIA DECOMPOSITION METHOD." Journal of Computer Science and Applied Mathematics 5, no. 2 (October 30, 2023): 145–53. http://dx.doi.org/10.37418/jcsam.5.2.7.

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The effect of the source, initial or boundary conditions in the use of Adomian decomposition method (ADM) on nonlinear partial differential equation or nonlinear equation in general is enormous. Sometimes the equation in question result to continuous exact solution in series form, other times it result to discrete approximate analytical solutions. In this paper, we show that continuous exact solitons can be obtained on application of ADM to the Fisher's equation with the deployment Taylor theorem to the terms(s) in question. And, the resulting series is split into the integral equations during the solution process. Resulting to multivariate Taylor's series of the exact solitons with the help of Adomian polynomials of the nonlinear reaction term correctly calculated. More physical results are further depicted in 2D, 3D and contour plots.

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Prokhorova, M. F. "Factorization of the reaction-diffusion equation, the wave equation, and other equations." Proceedings of the Steklov Institute of Mathematics 287, S1 (November 27, 2014): 156–66. http://dx.doi.org/10.1134/s0081543814090156.

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Huang, Qicai. "Adaptive Extraction of Oil Painting Texture Features Based on Reaction Diffusion Equation." Advances in Mathematical Physics 2021 (November 3, 2021): 1–11. http://dx.doi.org/10.1155/2021/4464985.

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The oil painting retrieval technology based on the reaction diffusion equation has attracted widespread attention in the fields of oil painting processing and pattern recognition. The description and extraction of oil painting information and the classification method of oil paintings are two important processes in content-based oil painting retrieval. Inspired by the restoration and decomposition functional model of equal oil painting, we propose a reaction diffusion equation model. The new model contains two reaction diffusion equations with different principal parts. One principal part is total variation diffusion, which is used to remove noise. The other main part is thermal diffusion, which is used to modify the source term of the denoising reaction-diffusion equation to achieve the effect of protecting the texture of the oil painting. The interaction of the two reaction-diffusion equations finally achieves denoising while maintaining the boundaries and textures. Under the framework of the above reaction diffusion equation model, we introduce Laplace flow to replace the original total variation flow, so that the new denoising reaction diffusion equation combines the isotropic diffusion and total variation flow of the thermal reaction diffusion equation to achieve the effect of adaptive theoretical research. Using regularization methods and methods, we, respectively, get the well-posedness of the two model solutions, which provides the necessary preparation for numerical calculations. Based on the statistical theory and classification principles of support vector machines, combined with the characteristics of oil painting classification, the research and analysis are carried out from the three important aspects of kernel function, training algorithm, and multiclass classifier algorithm that affect the classification effect and speed. Numerical experiments show that the given filter model has a better processing effect on images with different types and different degrees of noise pollution. On this basis, an oil painting classification system based on texture features is designed, combined with an improved gray-level cooccurrence matrix algorithm and a multiclass support vector machine classification model, to extract, train, and classify oil paintings. Experiments with three types of oil paintings prove that the system can achieve a good oil painting classification effect. Different from the original model, the new model is based on the framework of reaction-diffusion equations. In addition, the new model has good effects in removing step effects, maintaining boundaries and denoising, especially in maintaining texture.

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RODRIGO, M., and M. MIMURA. "ON SOME CLASSES OF LINEARIZABLE REACTION-CONVECTION-DIFFUSION EQUATIONS." Analysis and Applications 02, no. 01 (January 2004): 11–19. http://dx.doi.org/10.1142/s0219530504000266.

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In this paper, we consider the class of equations ut=[F(x,u)ux+G(x,u)]x+H(x,u). Using hodograph and dependent variable transformations, we determine sufficient conditions on F, G, and H such that this equation is linearizable. We also derive a general quasilinear equation, which includes the Clarkson–Fokas–Ablowitz equation (SIAM J. Appl. Math.49 (1989), 1188–1209), that can be transformed into semilinear form.

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Dissertations / Theses on the topic "Diffusion-reaction equation"

1

Yu, Weiming. "Identification of Coefficients in Reaction-Diffusion Equations." University of Cincinnati / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1076186036.

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Hellander, Stefan. "Stochastic Simulation of Reaction-Diffusion Processes." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-198522.

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Numerical simulation methods have become an important tool in the study of chemical reaction networks in living cells. Many systems can, with high accuracy, be modeled by deterministic ordinary differential equations, but other systems require a more detailed level of modeling. Stochastic models at either the mesoscopic level or the microscopic level can be used for cases when molecules are present in low copy numbers. In this thesis we develop efficient and flexible algorithms for simulating systems at the microscopic level. We propose an improvement to the Green's function reaction dynamics algorithm, an efficient microscale method. Furthermore, we describe how to simulate interactions with complex internal structures such as membranes and dynamic fibers. The mesoscopic level is related to the microscopic level through the reaction rates at the respective scale. We derive that relation in both two dimensions and three dimensions and show that the mesoscopic model breaks down if the discretization of space becomes too fine. For a simple model problem we can show exactly when this breakdown occurs. We show how to couple the microscopic scale with the mesoscopic scale in a hybrid method. Using the fact that some systems only display microscale behaviour in parts of the system, we can gain computational time by restricting the fine-grained microscopic simulations to only a part of the system. Finally, we have developed a mesoscopic method that couples simulations in three dimensions with simulations on general embedded lines. The accuracy of the method has been verified by comparing the results with purely microscopic simulations as well as with theoretical predictions.
eSSENCE

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Smith, Stephen. "Stochastic reaction-diffusion models in biology." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33142.

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Every cell contains several millions of diffusing and reacting biological molecules. The interactions between these molecules ultimately manifest themselves in all aspects of life, from the smallest bacterium to the largest whale. One of the greatest open scientific challenges is to understand how the microscopic chemistry determines the macroscopic biology. Key to this challenge is the development of mathematical and computational models of biochemistry with molecule-level detail, but which are sufficiently coarse to enable the study of large systems at the cell or organism scale. Two such models are in common usage: the reaction-diffusion master equation, and Brownian dynamics. These models are utterly different in both their history and in their approaches to chemical reactions and diffusion, but they both seek to address the same reaction-diffusion question. Here we make an in-depth study into the physical validity of these models under various biological conditions, determining when they can reliably be used. Taking each model in turn, we propose modifications to the models to better model the realities of the cellular environment, and to enable more efficient computational implementations. We use the models to make predictions about how and why cells behave the way they do, from mechanisms of self-organisation to noise reduction. We conclude that both models are extremely powerful tools for clarifying the details of the mysterious relationship between chemistry and biology.

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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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Meral, Gulnihal. "Numerical Solution Of Nonlinear Reaction-diffusion And Wave Equations." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/3/12610568/index.pdf.

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In this thesis, the two-dimensional initial and boundary value problems (IBVPs) and the one-dimensional Cauchy problems defined by the nonlinear reaction- diffusion and wave equations are numerically solved. The dual reciprocity boundary element method (DRBEM) is used to discretize the IBVPs defined by single and system of nonlinear reaction-diffusion equations and nonlinear wave equation, spatially. The advantage of DRBEM for the exterior regions is made use of for the latter problem. The differential quadrature method (DQM) is used for the spatial discretization of IBVPs and Cauchy problems defined by the nonlinear reaction-diffusion and wave equations. The DRBEM and DQM applications result in first and second order system of ordinary differential equations in time. These systems are solved with three different time integration methods, the finite difference method (FDM), the least squares method (LSM) and the finite element method (FEM) and comparisons among the methods are made. In the FDM a relaxation parameter is used to smooth the solution between the consecutive time levels. It is found that DRBEM+FEM procedure gives better accuracy for the IBVPs defined by nonlinear reaction-diffusion equation. The DRBEM+LSM procedure with exponential and rational radial basis functions is found suitable for exterior wave problem. The same result is also valid when DQM is used for space discretization instead of DRBEM for Cauchy and IBVPs defined by nonlinear reaction-diffusion and wave equations.

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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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Kieri, Emil. "Accuracy aspects of the reaction-diffusion master equation on unstructured meshes." Thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-145978.

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The reaction-diffusion master equation (RDME) is a stochastic model for spatially heterogeneous chemical systems. Stochastic models have proved to be useful for problems from molecular biology since copy numbers of participating chemical species often are small, which gives a stochastic behaviour. The RDME is a discrete space model, in contrast to spatially continuous models based on Brownian motion. In this thesis two accuracy issues of the RDME on unstructured meshes are studied. The first concerns the rates of diffusion events. Errors due to previously used rates are evaluated, and a second order accurate finite volume method, not previously used in this context, is implemented. The new discretisation improves the accuracy considerably, but unfortunately it puts constraints on the mesh, limiting its current usability. The second issue concerns the rates of bimolecular reactions. Using the macroscopic reaction coefficients these rates become too low when the spatial resolution is high. Recently, two methods to overcome this problem by calculating mesoscopic reaction rates for Cartesian meshes have been proposed. The methods are compared and evaluated, and are found to work remarkably well. Their possible extension to unstructured meshes is discussed.

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Lee, Isobel Micheline. "The existance of multiple steady-state solutions of a reaction-diffusion equation." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329934.

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Gibbs, Simon Paul. "Solutions of the reaction-diffusion eikonal equation on closed two-dimensional manifolds." Thesis, Glasgow Caledonian University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357134.

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Josien, Marc. "Etude mathématique et numérique de quelques modèles multi-échelles issus de la mécanique des matériaux." Thesis, Paris Est, 2018. http://www.theses.fr/2018PESC1120/document.

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Le travail de cette thèse a porté sur l'étude mathématique et numérique de quelques modèles multi-échelles issus de la physique des matériaux. La première partie de ce travail est consacrée à l'homogénéisation mathématique d'un problème elliptique avec une petite échelle. Nous étudions le cas particulier d'un matériau présentant une structure périodique avec un défaut. En adaptant la théorie classique d'Avellaneda et Lin pour les milieux périodiques, on démontre qu'on peut approximer finement la solution d'un tel problème, notamment à l'échelle microscopique. Nous obtenons des taux de convergence dépendant de l'étalement du défaut. On démontre aussi quelques propriétés des fonctions de Green d'un problème elliptique périodique avec conditions de bord périodiques. Les dislocations sont des lignes de défaut de la matière responsables du phénomène de plasticité. Les deuxième et troisième parties de ce mémoire portent sur la simulation de dislocations, d'abord en régime stationnaire puis en régime dynamique. Nous utilisons le modèle de Peierls, qui couple échelle atomique et échelle mésoscopique. Dans le cadre stationnaire, on obtient une équation intégrodifférentielle non-linéaire avec un laplacien fractionnaire: l'équation de Weertman. Nous en étudions les propriétés mathématiques et proposons un schéma numérique pour en approximer la solution. Dans le cadre dynamique, on obtient une équation intégrodifférentielle à la fois en temps et en espace. Nous en faisons une brève étude mathématique, et comparons différents algorithmes pour la simuler. Enfin, dans la quatrième partie, nous étudions la limite macroscopique d'une chaîne d'atomes soumis à la loi de Newton. Des arguments formels suggèrent que celle-ci devrait être décrite par une équation des ondes non-linéaires. Or, nous démontrons --sous certaines hypothèses-- qu'il n'en est rien lorsque des chocs apparaissent
In this thesis we study mathematically and numerically some multi-scale models from materials science. First, we investigate an homogenization problem for an oscillating elliptic equation. The material under consideration is described by a periodic structure with a defect at the microscopic scale. By adapting Avellaneda and Lin's theory for periodic structures, we prove that the solution of the oscillating equation can be approximated at a fine scale. The rates of convergence depend upon the integrability of the defect. We also study some properties of the Green function of periodic materials with periodic boundary conditions. Dislocations are lines of defects inside materials, which induce plasticity. The second part and the third part of this manuscript are concerned with simulation of dislocations, first in the stationnary regime then in the dynamical regime. We use the Peierls model, which couples atomistic and mesoscopic scales and involves integrodifferential equations. In the stationary regime, dislocations are described by the so-called Weertman equation, which is nonlinear and involves a fractional Laplacian. We study some mathematical properties of this equation and propose a numerical scheme for approximating its solution. In the dynamical regime, dislocations are described by an equation which is integrodifferential in time and space. We compare some numerical methods for recovering its solution. In the last chapter, we investigate the macroscopic limit of a simple chain of atoms governed by the Newton equation. Surprisingly enough, under technical assumptions, we show that it is not described by a nonlinear wave equation when shocks occur

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Books on the topic "Diffusion-reaction equation"

1

Elementary feedback stabilization of the linear reaction-convection-diffusion equation and the wave equation. Heidelberg: Springer, 2010.

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A, Doelman, ed. The dynamics of modulated wave trains. Providence, R.I: American Mathematical Society, 2009.

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Banks, Stephen P. Boundary stabilization of the reaction-diffusion equation with unilateral conditions. Sheffield: University of Sheffield, Dept. of Control Engineering, 1987.

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H, Carpenter Mark, and Langley Research Center, eds. Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 2001.

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H, Carpenter Mark, and Langley Research Center, eds. Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 2001.

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H, Carpenter Mark, and Langley Research Center, eds. Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 2001.

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Liu, Weijiu. Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-04613-1.

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C, Sorensen D., and Institute for Computer Applications in Science and Engineering., eds. An asymptotic induced numerical method for the convection-diffusion-reaction equation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1988.

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Codina, R. Comparison of some finite element methods for solving the diffusion-convection-reaction equation. Barcelona, Spain: International Center for Numerical Methods in Engineering, 1996.

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Ughi, Maura. On the porous media equation with either source or absorption. Rosario, República Argentina: Universidad Nacional de Rosario, Facultad de Ciencias Exactas, Ingenieria y Agrimensura, 1991.

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Book chapters on the topic "Diffusion-reaction equation"

1

Clairambault, Jean. "Reaction-Diffusion-Advection Equation." In Encyclopedia of Systems Biology, 1817. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_697.

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Viehland, Larry A. "The Boltzmann Equation." In Gaseous Ion Mobility, Diffusion, and Reaction, 117–26. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04494-7_4.

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Liu, Weijiu. "Linear Reaction-Convection-Diffusion Equation." In Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation, 119–214. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-04613-1_4.

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Viehland, Larry A. "Moment Methods for Solving the Boltzmann Equation." In Gaseous Ion Mobility, Diffusion, and Reaction, 127–54. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04494-7_5.

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Horgmo Jæger, Karoline, and Aslak Tveito. "A Simple Cable Equation." In Differential Equations for Studies in Computational Electrophysiology, 47–52. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30852-9_6.

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AbstractThe cable equation was first derived to model transport of electrical signals in telegraphic cables. But it later gained enormous popularity as a model of transport of electrical signals along a neuronal axon. In Chapter 9, we will discuss how this equation is derived and how the different terms in the equation come about. But here, we will just take a simple version of the equations for granted and then try to solve them. We will observe that the few techniques we learned above are actually sufficient to solve the non-linear reaction-diffusion equations we consider here.

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Constantin, P., C. Foias, B. Nicolaenko, and R. Teman. "Application: The Chaffee—Infante Reaction—Diffusion Equation." In Applied Mathematical Sciences, 111–18. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3506-4_20.

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Levi, Decio, Miguel A. Rodríguez, and Zora Thomova. "Conditional Discretization of a Generalized Reaction–Diffusion Equation." In Quantum Theory and Symmetries, 149–56. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55777-5_14.

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Saxena, R. K., A. M. Mathai, and H. J. Haubold. "Solutions of the Fractional Reaction Equation and the Fractional Diffusion Equation." In Astrophysics and Space Science Proceedings, 53–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03325-4_7.

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Amattouch, M. R., and H. Belhadj. "An Heuristic Scheme for a Reaction Advection Diffusion Equation." In Heuristics for Optimization and Learning, 223–38. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58930-1_15.

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Bellettini, Giovanni. "One-dimensional analysis related to a reaction-diffusion equation." In Lecture Notes on Mean Curvature Flow, Barriers and Singular Perturbations, 229–47. Pisa: Scuola Normale Superiore, 2013. http://dx.doi.org/10.1007/978-88-7642-429-8_15.

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Conference papers on the topic "Diffusion-reaction equation"

1

Yanagida, Eiji. "DYNAMICS OF GLOBAL SOLUTIONS OF A SEMILINEAR PARABOLIC EQUATION." In The International Conference on Reaction-Diffusion System and Viscosity Solutions. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812834744_0014.

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Alberdi Celaya, Elisabete, and Judit Muñoz Matute. "MODELLING GLIOMAS USING THE REACTION-DIFFUSION EQUATION." In 10th annual International Conference of Education, Research and Innovation. IATED, 2017. http://dx.doi.org/10.21125/iceri.2017.0977.

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Wei, Guo W. "Generalized reaction-diffusion equation for image processing." In SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, edited by Franklin T. Luk. SPIE, 1999. http://dx.doi.org/10.1117/12.367626.

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CARINI, M., and N. MANGANARO. "EXACT SOLUTIONS OF A REACTION DIFFUSION EQUATION." In In Honor of the 65th Birthday of Antonio Greco. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708908_0005.

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Imamura, Kouya, and Kunimochi Sakamoto. "TRAVELLING PULSE WAVES NON-VANISHING AT INFINITY FOR THE DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION." In The International Conference on Reaction-Diffusion System and Viscosity Solutions. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812834744_0010.

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Guo, Chunli, and Chengkang Xie. "Stabilization of spatially non-causal reaction-diffusion equation." In 2012 24th Chinese Control and Decision Conference (CCDC). IEEE, 2012. http://dx.doi.org/10.1109/ccdc.2012.6244291.

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Curilef, Sergio. "Analytical solutions for a nonlinear reaction-diffusion equation." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825867.

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Ma, Jianwei. "Image assimilation by geometric wavelet based reaction-diffusion equation." In Optical Engineering + Applications, edited by Dimitri Van De Ville, Vivek K. Goyal, and Manos Papadakis. SPIE, 2007. http://dx.doi.org/10.1117/12.733054.

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KABIR MAHAMAN, M., and M. NORBERT HOUNKONNOU. "ANALYTICAL SOLUTIONS OF A GENERALIZED NONLINEAR REACTION-DIFFUSION EQUATION." In Proceedings of the Fourth International Workshop. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812773241_0010.

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Khalid, Nor Farah Wahidah Nor, Mohd Almie Alias, and Ishak Hashim. "Modelling adaptive therapy for tumor using reaction-diffusion equation." In 4TH SYMPOSIUM ON INDUSTRIAL SCIENCE AND TECHNOLOGY (SISTEC2022). AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0171688.

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Reports on the topic "Diffusion-reaction equation"

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Manzini, Gianmarco, Andrea Cangiani, and Oliver Sutton. The Conforming Virtual Element Method for the convection-diffusion-reaction equation with variable coeffcients. Office of Scientific and Technical Information (OSTI), October 2014. http://dx.doi.org/10.2172/1159207.

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Manzini, Gianmarco, Andrea Cangiani, and Oliver Sutton. Numerical results using the conforming VEM for the convection-diffusion-reaction equation with variable coefficients. Office of Scientific and Technical Information (OSTI), October 2014. http://dx.doi.org/10.2172/1159206.

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Hindmarsh, A. Index and consistency analysis for DAE (differential-algebraic equation) systems for Stefan-Maxwell diffusion-reaction problems. Office of Scientific and Technical Information (OSTI), March 1990. http://dx.doi.org/10.2172/6934906.

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Wang, Chi-Jen. Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport. Office of Scientific and Technical Information (OSTI), January 2013. http://dx.doi.org/10.2172/1226552.

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Hale, Jack K., and Kunimochi Sakamoto. Shadow Systems and Attractors in Reaction-Diffusion Equations,. Fort Belvoir, VA: Defense Technical Information Center, April 1987. http://dx.doi.org/10.21236/ada185804.

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Fields, Mary A. Modeling Large Scale Troop Movement Using Reaction Diffusion Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1993. http://dx.doi.org/10.21236/ada270701.

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Heineike, Benjamin M. Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods. Fort Belvoir, VA: Defense Technical Information Center, May 2002. http://dx.doi.org/10.21236/ada403766.

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