Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F15%3A43926099" target="_blank" >RIV/49777513:23520/15:43926099 - isvavai.cz</a>
Result on the web
<a href="http://www.hindawi.com/journals/ddns/2015/791304/" target="_blank" >http://www.hindawi.com/journals/ddns/2015/791304/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1155/2015/791304" target="_blank" >10.1155/2015/791304</a>

Result language
angličtina
Original language name
Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA15-07690S" target="_blank" >GA15-07690S: Partial Difference and Differential Equations on Lattices</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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