Construction of eternal solutions for a semilinear parabolic equation

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dc.creatorRobinson, Michael
dc.date2008-05-06
dc.date.accessioned2026-07-07T09:37:18Z
dc.date.available2026-07-07T09:37:18Z
dc.descriptionEternal solutions of parabolic equations (those which are defined for all time) are typically rather rare. For example, the heat equation has exactly one eternal solution -- the trivial solution. While solutions to the heat equation exist for all forward time, they cannot be extended backwards in time. Nonlinearities exasperate the situation somewhat, in that solutions may form singularities in both backward and forward time. However, semilinear parabolic equations can also support nontrivial eternal solutions. This article shows how nontrivial eternal solutions can be constructed for a semilinear equation that has at least two distinct equilibrium solutions. The resulting eternal solution is a heteroclinic orbit which connects the two given equilibria.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/0805.0750
dc.identifierhttp://arxiv.org/abs/0805.0750
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160414
dc.subjectAnalysis of PDEs
dc.subject35B40; 35K55
dc.titleConstruction of eternal solutions for a semilinear parabolic equation
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