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

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/86116

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor	Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions
dc.contributor.author	Von Below, Joachim
dc.contributor.author	Lubary Martínez, José Antonio
dc.date	2015-09-01
dc.identifier.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.
dc.identifier.citation	1422-6383
dc.identifier.citation	10.1007/s00025-014-0429-8
dc.identifier.uri	http://hdl.handle.net/2117/86116
dc.language.iso	eng
dc.relation	http://link.springer.com/article/10.1007%2Fs00025-014-0429-8
dc.relation	info:eu-repo/grantAgreement/ES/6PN/MTM2011-27739-C04-01
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject	Reaction-diffusion-equations
dc.subject	metric graphs
dc.subject	networks
dc.subject	attractors
dc.subject	stability
dc.subject	double-well potential
dc.subject	Classificació AMS::05 Combinatorics::05C Graph theory
dc.title	Instability of stationary solutions of reaction-diffusion-equations on graphs
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.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 balanced autonomous case is discussed on the two-sided unbounded path with equal edge lengths.
dc.description.abstract	Peer Reviewed

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