To access the full text documents, please follow this link:

Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier
Cabré Vilagut, Xavier; Martel, Yvan
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
In 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.
Parabolic partial differential equations
Partial differential equations
linear heat equations
singular potentials
Equacions en derivades parcials
Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
Attribution-NonCommercial-NoDerivs 2.5 Spain

Show full item record

Related documents

Other documents of the same author

Cabré Vilagut, Xavier; Roquejoffre, Jean-Michel
Cabré Vilagut, Xavier; Roquejoffre, Jean-Michel