An Lp approach to a parabolic problem with blowing up solutions

Abstract

We want to examine the simple exemplary nonlinear parabol i c equation (1) ut = A u + A | a | q ~ 1 c i t A>0, q> 1, considered with the Dirichlet or Neumann type boundary condit i o n s : (2) u(0,x) = ^ ( x ) , xeftcR0, ( 3 ' ) u(t,x) = 0 for x e 3ft, or (3") =0 for x e 9 f t , where £ i s a bounded smooth (8fteC^+^ with some |5 e ( 0 , l ) ) domain, t » 0 and n denotes the inward normal vector to 3ft (Fragment tekstu).