Invariant regions for systems of lattice reaction-diffusion equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10366140" target="_blank" >RIV/00216208:11320/17:10366140 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jde.2017.08.019" target="_blank" >http://dx.doi.org/10.1016/j.jde.2017.08.019</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2017.08.019" target="_blank" >10.1016/j.jde.2017.08.019</a>

Result language
angličtina
Original language name
Invariant regions for systems of lattice reaction-diffusion equations
Original language description
In this paper, we study systems of lattice differential equations of reaction diffusion type. First, we establish some basic properties such as the local existence and global uniqueness of bounded solutions. Then we proceed to our main goal, which is the study of invariant regions. Our main result can be interpreted as an analogue of the weak maximum principle for systems of lattice differential equations. It is inspired by existing results for parabolic differential equations, but its proof is different and relies on the Euler approximations of solutions to lattice differential equations. As a corollary, we obtain a global existence theorem for nonlinear systems of lattice reaction diffusion equations. The results are illustrated on examples from population dynamics.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

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
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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