Exponential number of stationary solutions for Nagumo equations on graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F17%3A43932201" target="_blank" >RIV/49777513:23520/17:43932201 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0022247X17306376" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0022247X17306376</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2017.06.075" target="_blank" >10.1016/j.jmaa.2017.06.075</a>
Alternative languages
Result language
angličtina
Original language name
Exponential number of stationary solutions for Nagumo equations on graphs
Original language description
We study the Nagumo reaction–diffusion equation on graphs and its dependence on the underlying graph structure and reaction–diffusion parameters. We provide necessary and sufficient conditions for the existence and nonexistence of spatially heterogeneous stationary solutions. Furthermore, we observe that for sufficiently strong reactions (or sufficiently weak diffusion) there are $3^n$ stationary solutions out of which $2^n$ are asymptotically stable. Our analysis reveals interesting relationship between the analytic properties (diffusion and reaction parameters) and various graph characteristics (degree distribution, graph diameter, eigenvalues). We illustrate our results by a detailed analysis of the Nagumo equation on a simple graph and conclude with a list of open questions.
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
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 Mathematical Analysis and Applications
ISSN
0022-247X
e-ISSN
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Volume of the periodical
455
Issue of the periodical within the volume
1-2
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
16
Pages from-to
1749-1764
UT code for WoS article
000406568800051
EID of the result in the Scopus database
2-s2.0-85021706012