Reaction-diffusion equations on graphs: stationary states and Lyapunov functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438138" target="_blank" >RIV/00216208:11320/21:10438138 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ms_FHHKm5X" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ms_FHHKm5X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1361-6544/abd52c" target="_blank" >10.1088/1361-6544/abd52c</a>

Result language
angličtina
Original language name
Reaction-diffusion equations on graphs: stationary states and Lyapunov functions
Original language description
Reaction-diffusion equations on graphs (networks) serve as mathematical models of various phenomena in physics and biology. We study the existence of spatially heterogeneous stationary states, provided that the diffusion coefficients are sufficiently small. We provide an easily applicable criterion for determining which of them are nonnegative. Next, we consider the problem of constructing Lyapunov functions for reaction-diffusion equations on graphs, provided that a Lyapunov function for the corresponding non-diffusive system is known. We provide an easy-to-use result applicable in situations where the non-diffusive Lyapunov function is a sum of univariate functions with nondecreasing derivatives. The results are illustrated by means of several examples from mathematical biology.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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