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Mathematical Problems in Engineering
Volume 2014, Article ID 764248, 6 pages
http://dx.doi.org/10.1155/2014/764248
Research Article

Lower Bounds Estimate for the Blow-Up Time of a Slow Diffusion Equation with Nonlocal Source and Inner Absorption

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

Received 24 July 2013; Accepted 20 December 2013; Published 2 January 2014

Academic Editor: Mufid Abudiab

Copyright © 2014 Zhong Bo Fang et al. 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 a slow diffusion equation with nonlocal source and inner absorption subject to homogeneous Dirichlet boundary condition or homogeneous Neumann boundary condition. Based on an auxiliary function method and a differential inequality technique, lower bounds for the blow-up time are given if the blow-up occurs in finite time.