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2018 Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities
Jamal H. Al-Smail, Salim A. Messaoudi, Ala A. Talahmeh
Int. J. Differ. Equ. 2018(SI2): 1-9 (2018). DOI: 10.1155/2018/9754567

Abstract

We consider the following nonlinear parabolic equation: ut-div(|u|p(x)-2u)=f(x,t), where f:Ω×(0,T)R and the exponent of nonlinearity p(·) are given functions. By using a nonlinear operator theory, we prove the existence and uniqueness of weak solutions under suitable assumptions. We also give a two-dimensional numerical example to illustrate the decay of solutions.

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Jamal H. Al-Smail. Salim A. Messaoudi. Ala A. Talahmeh. "Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities." Int. J. Differ. Equ. 2018 (SI2) 1 - 9, 2018. https://doi.org/10.1155/2018/9754567

Information

Received: 11 October 2017; Accepted: 25 December 2017; Published: 2018
First available in Project Euclid: 12 April 2018

zbMATH: 06915965
MathSciNet: MR3773444
Digital Object Identifier: 10.1155/2018/9754567

Rights: Copyright © 2018 Hindawi

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Vol.2018 • No. SI2 • 2018
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