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Abstract and Applied Analysis
Volume 2014, Article ID 241650, 9 pages
http://dx.doi.org/10.1155/2014/241650
Research Article

Global and Blow-Up Solutions for a Class of Nonlinear Parabolic Problems under Robin Boundary Condition

Department of Mathematics, Taiyuan University of Technology, Shanxi 030024, China

Received 26 June 2014; Accepted 28 July 2014; Published 14 August 2014

Academic Editor: Sanling Yuan

Copyright © 2014 Lingling Zhang and Hui Wang. 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 discuss the global and blow-up solutions of the following nonlinear parabolic problems with a gradient term under Robin boundary conditions: , in , , on , , in , where is a bounded domain with smooth boundary . Under some appropriate assumption on the functions , , , , and and initial value , we obtain the sufficient conditions for the existence of a global solution, an upper estimate of the global solution, the sufficient conditions for the existence of a blow-up solution, an upper bound for “blow-up time,” and an upper estimate of “blow-up rate.” Our approach depends heavily on the maximum principles.