Blow up for some nonlinear parabolic problems with convection under dynamical boundary conditions
Résumé
Blow up phenomena for solutions of nonlinear parabolic problems
including a convection term ∂tu = div(a(x)∇u) + f (x, t, u, ∇u) in a bounded
domain under dissipative dynamical time lateral boundary conditions σ∂tu +
∂ν u = 0 are investigated. It turns out that under natural assumptions in
the proper superlinear case no global weak solutions can exist. Moreover,
for certain classes of nonlinearities the blow up times can be estimated from
above as in the reaction diffusion case [6]. Finally, as a model case including a
sign change of the convection term, the occurrence of blow up is investigated
for the one–dimensional equation ∂tu = ∂2
xu − u∂xu + up
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
---|