Show simple item record

dc.contributor.authorCabré Vilagut, Xavier
dc.contributor.authorMartel, Yvan
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.description.abstractIn this Note, we consider the linear heat equation ut - Au= a(x)u in (0,T)xW,u=0 on (0,T)xaW, and u(0)=uº on W, where W C RN is a smooth bounded domain. We assume that a€L^loc(W) a >=0 and u>=. A simple condition on the potential a is necessary and suficient for the existence of positive weak solutions that are global in time and grow at most exponentially in time. We show that this condition, based on the existence of a Hardy type inequality with weight a(x), is "almost" necessary for the local existence in time of positive weak solutions. Applying these results to some "critical" potentials, we find new results on existence and on instantaneous and complete blow-up of solutions.
dc.format.extent6 pages
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subject.lcshParabolic partial differential equations
dc.subject.lcshPartial differential equations
dc.subject.otherlinear heat equations
dc.subject.othersingular potentials
dc.titleExistence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier
dc.subject.lemacEquacions en derivades parcials
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.subject.amsClassificació AMS::35 Partial differential equations::35K Parabolic equations and systems
dc.subject.amsClassificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
dc.rights.accessOpen Access

Files in this item


This item appears in the following Collection(s)

Show simple item record

Attribution-NonCommercial-NoDerivs 2.5 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 2.5 Spain