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

Author
Von Below, J.; Lubary, J.
Type of activity
Journal article
Journal
Results in mathematics
Date of publication
2015-09-01
Volume
68
Number
1
First page
171
Last page
201
DOI
https://doi.org/10.1007/s00025-014-0429-8 Open in new window
Project funding
Ecuaciones en derivadas parciales: problemas de reacción-difusión y problemas geométricos
Repository
http://hdl.handle.net/2117/86116 Open in new window
URL
http://link.springer.com/article/10.1007%2Fs00025-014-0429-8 Open in new window
Abstract
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...
Citation
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.
Keywords
Reaction-diffusion-equations, attractors, double-well potential, metric graphs, networks, stability
Group of research
EDP - Partial Differential Equations and Applications

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