Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation

Petr Stehlík and Jonáš Volek

Discrete Dynamics in Nature and Society, 2015, vol. 2015, 1-13

Abstract:

We study reaction-diffusion equations with a general reaction function on one-dimensional lattices with continuous or discrete time , . We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time) exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:791304

DOI: 10.1155/2015/791304

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