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Journal of Function Spaces
Volume 2016, Article ID 8107657, 7 pages
http://dx.doi.org/10.1155/2016/8107657
Research Article

Blow-Up Phenomena for Nonlinear Reaction-Diffusion Equations under Nonlinear Boundary Conditions

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

Received 20 November 2015; Accepted 6 March 2016

Academic Editor: Leszek Olszowy

Copyright © 2016 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

This paper deals with blow-up and global solutions of the following nonlinear reaction-diffusion equations under nonlinear boundary conditions: where is a bounded domain with smooth boundary . We obtain the conditions under which the solutions either exist globally or blow up in a finite time by constructing auxiliary functions and using maximum principles. Moreover, the upper estimates of the “blow-up time,” the “blow-up rate,” and the global solutions are also given.