Initial blow-up of solutions of semilinear parabolic inequalities | Academic Article individual record
abstract

We study classical nonnegative solutions u(x,t) of the semilinear parabolic inequalities. 0ut-uupin (0,1) where p is a positive constant and is a bounded domain in Rn, n1. We show that a necessary and sufficient condition on p for such solutions u to satisfy a pointwise a priori bound on compact subsets K of as t0+ is p1+2/n and in this case the bound on u is. maxxKu(x,t)=O(t-n/2)as t0+. If in addition, is smooth, u satisfies the boundary condition u=0 on (0,1), and p<1+2/n, then we obtain a bound for u on the entire set as t0+. 2010 Elsevier Inc.

publication outlet

Journal of Differential Equations

author list (cited authors)
Taliaferro, S. D.
publication date
2011
publisher
Elsevier bv Publisher
keywords
  • Initial Blow-up
  • Semilinear Parabolic Inequalities
citation count

4

identifier
165419SE
Digital Object Identifier (DOI)
start page
892
end page
928
volume
250
issue
2