Well-posedness and maximum principles for lattice reaction-diffusion equations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10405683" target="_blank" >RIV/00216208:11320/19:10405683 - isvavai.cz</a>
Alternative codes found
RIV/49777513:23520/19:43954782
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cbBUtnu.Hf" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cbBUtnu.Hf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/anona-2016-0116" target="_blank" >10.1515/anona-2016-0116</a>
Alternative languages
Result language
angličtina
Original language name
Well-posedness and maximum principles for lattice reaction-diffusion equations
Original language description
Existence, uniqueness and continuous dependence results together with maximum principles represent key tools in the analysis of lattice reaction-diffusion equations. In this paper, we study these questions in full generality by considering nonautonomous reaction functions, possibly nonsymmetric diffusion and continuous, discrete or mixed time. First, we prove the local existence and global uniqueness of bounded solutions, as well as the continuous dependence of solutions on the underlying time structure and on initial conditions. Next, we obtain the weak maximum principle which enables us to get the global existence of solutions. Finally, we provide the strong maximum principle which exhibits an interesting dependence on the time structure. Our results are illustrated by the autonomous Fisher and Nagumo lattice equations and a nonautonomous logistic population model with a variable carrying capacity.
Czech name
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Czech description
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Classification
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
Result continuities
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)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Nonlinear Analysis
ISSN
2191-9496
e-ISSN
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Volume of the periodical
8
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
20
Pages from-to
303-322
UT code for WoS article
000459891200016
EID of the result in the Scopus database
2-s2.0-85020283199