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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 289245, 8 pages
http://dx.doi.org/10.1155/2014/289245
Research Article

Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China

Received 24 February 2014; Revised 11 April 2014; Accepted 11 April 2014; Published 30 April 2014

Academic Editor: Zhi-Bo Huang

Copyright © 2014 Zhong Bo Fang and Yan Chai. 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 investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee that exists globally or blows up at some finite time . Moreover, an upper bound for is derived. Under somewhat more restrictive conditions, a lower bound for is also obtained.