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.
Journal of Differential Equations
- Initial Blow-up
- Semilinear Parabolic Inequalities