Abstract and Applied Analysis
Volume 2010 (2010), Article ID 680572, 12 pages
doi:10.1155/2010/680572
Research Article

On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition

Zhilei Liang

School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China

Received 9 June 2010; Accepted 15 September 2010

Academic Editor: Nicholas Alikakos

Copyright © 2010 Zhilei Liang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We identify the blow-up set of solutions to the problem ut=(|ux|p-2ux)x, x>0, t∈(0,T), -|ux|p-2ux(0,t)=up-1(0,t), t∈(0,T), and u(x,0)=u0(x)≥0, x>0, where p>2. We obtain that the blow up set B(u) satisfies [0,p(p-1)/(p-2))⊂B(u)⊂[0,p(p-1)/(p-2)]. The proof is based on the analysis of the asymptotic behavior of self-similar representation and on the comparison methods.