![](/images/graphics-bg.png)
Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation
Joint Authors
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-09-30
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
We study reaction-diffusion equations with a general reaction function f on one-dimensional lattices with continuous or discrete time ux′ (or Δtux)=k(ux-1-2ux+ux+1)+f(ux), x∈Z.
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.
American Psychological Association (APA)
Stehlík, Petr& Volek, Jonáš. 2015. Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation. Discrete Dynamics in Nature and Society،Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1060768
Modern Language Association (MLA)
Stehlík, Petr& Volek, Jonáš. Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation. Discrete Dynamics in Nature and Society No. 2015 (2015), pp.1-13.
https://search.emarefa.net/detail/BIM-1060768
American Medical Association (AMA)
Stehlík, Petr& Volek, Jonáš. Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation. Discrete Dynamics in Nature and Society. 2015. Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1060768
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1060768