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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 532935, 12 pages
http://dx.doi.org/10.1155/2013/532935
Research Article

Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition

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

Received 14 July 2013; Accepted 18 September 2013

Academic Editor: Shaoyong Lai

Copyright © 2013 Zhong Bo Fang and Liru Qiu. 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 work is concerned with a mixed boundary value problem for the semilinear parabolic equation with a memory term and generalized Lewis functions which depends on both spacial variable and time. Under suitable conditions, we prove the existence and uniqueness of global solutions and the energy functional decaying exponentially or polynomially to zero as the time goes to infinity by introducing brief Lyapunov function and precise priori estimates.