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Instability of stationary solutions of reaction-diffusion-equations on graphs

Autor
Von Below, J.; Lubary, J.
Tipus d'activitat
Article en revista
Revista
Results in mathematics
Data de publicació
2015-09-01
Volum
68
Número
1
Pàgina inicial
171
Pàgina final
201
DOI
https://doi.org/10.1007/s00025-014-0429-8 Obrir en finestra nova
Projecte finançador
Ecuaciones en derivadas parciales: problemas de reacción-difusión y problemas geométricos
Repositori
http://hdl.handle.net/2117/86116 Obrir en finestra nova
URL
http://link.springer.com/article/10.1007%2Fs00025-014-0429-8 Obrir en finestra nova
Resum
The nonexistence of stable stationary nonconstant solutions of reaction-diffusion-equations partial derivative(t)u(j) = partial derivative(j)(a(j)(x(j))partial derivative(j)u(j)) + f(j)(u(j)) on the edges of a finite (topological) graph is investigated under continuity and consistent Kirchhoff flow conditions at all vertices of the graph. In particular, it is shown that in the balanced autonomous case f(u) = u - u(3), no such stable stationary solution can exist on any finite graph. Finally, the...
Citació
Von Below, J., Lubary, J. Instability of stationary solutions of reaction-diffusion-equations on graphs. "Results in mathematics", 01 Setembre 2015, vol. 68, núm. 1, p. 171-201.
Paraules clau
Reaction-diffusion-equations, attractors, double-well potential, metric graphs, networks, stability
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

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