Initial blow-up of solutions of semilinear parabolic inequalities Academic Article

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.

authors

• Taliaferro, Steven

published proceedings

• JOURNAL OF DIFFERENTIAL EQUATIONS

author list (cited authors)

• Taliaferro, S. D.

citation count

• 4

complete list of authors

• Taliaferro, Steven D

publication date

• January 2011

publisher

• Elsevier  Publisher

published in

• Journal of Differential Equations  Journal

keywords

• Initial Blow-up
• Semilinear Parabolic Inequalities

Digital Object Identifier (DOI)

• 10.1016/j.jde.2010.07.033

start page

• 892

end page

• 928

volume

• 250

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.jde.2010.07.033