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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 643819, 5 pages
http://dx.doi.org/10.1155/2013/643819
Research Article

Blow-Up in a Slow Diffusive -Laplace Equation with the Neumann Boundary Conditions

1Department of Mathematics, Dalian Nationalities University, Dalian 116600, China
2School of Science, East China Institute of Technology, Nanchang 330013, China
3School of Science, Dalian Jiaotong University, Dalian 116028, China

Received 4 April 2013; Accepted 4 June 2013

Academic Editor: Daniel C. Biles

Copyright © 2013 Chengyuan Qu and Bo 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 study a slow diffusive -Laplace equation in a bounded domain with the Neumann boundary conditions. A natural energy is associated to the equation. It is shown that the solution blows up in finite time with the nonpositive initial energy, based on an energy technique. Furthermore, under some assumptions of initial data, we prove that the solutions with bounded initial energy also blow up.