## Abstract and Applied Analysis

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

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 532935, 12 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393443512

Digital Object Identifier
doi:10.1155/2013/532935

Mathematical Reviews number (MathSciNet)
MR3126756

Zentralblatt MATH identifier
1293.35145

#### Citation

Fang, Zhong Bo; Qiu, Liru. Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 532935, 12 pages. doi:10.1155/2013/532935. https://projecteuclid.org/euclid.aaa/1393443512

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