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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 324857, 9 pages
http://dx.doi.org/10.1155/2014/324857
Research Article

Blow-Up Solutions and Global Existence for Quasilinear Parabolic Problems with Robin Boundary Conditions

School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

Received 30 October 2013; Accepted 18 February 2014; Published 30 March 2014

Academic Editor: Muhammad Usman

Copyright © 2014 Juntang Ding. 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 the blow-up and global solutions for a class of quasilinear parabolic problems with Robin boundary conditions. By constructing auxiliary functions and using maximum principles, the sufficient conditions for the existence of blow-up solution, an upper bound for the “blow-up time,” an upper estimate of the “blow-up rate,” the sufficient conditions for the existence of global solution, and an upper estimate of the global solution are specified.