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Instability of stationary solutions of reaction-diffusion-equations on graphs
dc.contributor.author | Von Below, Joachim |
dc.contributor.author | Lubary Martínez, José Antonio |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2016-04-22T17:54:59Z |
dc.date.issued | 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.issn | 1422-6383 |
dc.identifier.uri | http://hdl.handle.net/2117/86116 |
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.format.extent | 31 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.other | Reaction-diffusion-equations |
dc.subject.other | metric graphs |
dc.subject.other | networks |
dc.subject.other | attractors |
dc.subject.other | stability |
dc.subject.other | double-well potential |
dc.title | Instability of stationary solutions of reaction-diffusion-equations on graphs |
dc.type | Article |
dc.contributor.group | Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions |
dc.identifier.doi | 10.1007/s00025-014-0429-8 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::05 Combinatorics::05C Graph theory |
dc.relation.publisherversion | http://link.springer.com/article/10.1007%2Fs00025-014-0429-8 |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 16942908 |
dc.description.version | Postprint (published version) |
dc.relation.projectid | info:eu-repo/grantAgreement/MICINN//MTM2011-27739-C04-01/ES/ECUACIONES EN DERIVADAS PARCIALES: PROBLEMAS DE REACCION-DIFUSION Y PROBLEMAS GEOMETRICOS/ |
dc.date.lift | 10000-01-01 |
local.citation.author | Von Below, J.; Lubary, J. |
local.citation.publicationName | Results in mathematics |
local.citation.volume | 68 |
local.citation.number | 1 |
local.citation.startingPage | 171 |
local.citation.endingPage | 201 |
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