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

doi:10.1155/2018/9754567

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We consider the following nonlinear parabolic equation: ut-div(up(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.

Original language	English
Article number	9754567
Journal	International Journal of Differential Equations
Volume	2018
DOIs	https://doi.org/10.1155/2018/9754567
State	Published - 2018

Bibliographical note

Publisher Copyright:
© 2018 Jamal H. Al-Smail et al.

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1155/2018/9754567

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title = "Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities",

abstract = "We consider the following nonlinear parabolic equation: ut-div(up(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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AU - Al-Smail, Jamal H.

AU - Messaoudi, Salim A.

AU - Talahmeh, Ala A.

PY - 2018

Y1 - 2018

N2 - We consider the following nonlinear parabolic equation: ut-div(up(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.

AB - We consider the following nonlinear parabolic equation: ut-div(up(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.

UR - https://www.scopus.com/pages/publications/85042779433

U2 - 10.1155/2018/9754567

DO - 10.1155/2018/9754567

M3 - Article

AN - SCOPUS:85042779433

SN - 1687-9643

VL - 2018

JO - International Journal of Differential Equations

JF - International Journal of Differential Equations

M1 - 9754567

ER -

Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities

Abstract

Bibliographical note

ASJC Scopus subject areas

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