Invariant regions for systems of lattice reaction-diffusion equations
Result 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.
Keywords
Existence and uniquenessMaximum principleInvariant regionReaction diffusion equationLattice differential equation
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
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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Classification
Type
Jimp - 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
Result continuities
Project
GA15-07690S: Partial Difference and Differential Equations on Lattices
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Differential Equations
ISSN
0022-0396
e-ISSN
—
Volume of the periodical
263
Issue of the periodical within the volume
11
Country of publishing house
US - UNITED STATES
Number of pages
26
Pages from-to
7601-7626
UT code for WoS article
000412863000020
EID of the result in the Scopus database
2-s2.0-85027724835
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2017