Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities
We consider the following nonlinear parabolic equation: ut-div(|∇u|p(x)-2∇u)=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 t...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2018/9754567 |
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| _version_ | 1832552888033869824 |
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| author | Jamal H. Al-Smail Salim A. Messaoudi Ala A. Talahmeh |
| author_facet | Jamal H. Al-Smail Salim A. Messaoudi Ala A. Talahmeh |
| author_sort | Jamal H. Al-Smail |
| collection | DOAJ |
| description | We consider the following nonlinear parabolic equation: ut-div(|∇u|p(x)-2∇u)=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. |
| format | Article |
| id | doaj-art-f4c1d48a7b75439085794a1b72cdb618 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-f4c1d48a7b75439085794a1b72cdb6182025-02-03T05:57:36ZengWileyInternational Journal of Differential Equations1687-96431687-96512018-01-01201810.1155/2018/97545679754567Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent NonlinearitiesJamal H. Al-Smail0Salim A. Messaoudi1Ala A. Talahmeh2Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 546, Dhahran 31261, Saudi ArabiaDepartment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 546, Dhahran 31261, Saudi ArabiaDepartment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 546, Dhahran 31261, Saudi ArabiaWe consider the following nonlinear parabolic equation: ut-div(|∇u|p(x)-2∇u)=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.http://dx.doi.org/10.1155/2018/9754567 |
| spellingShingle | 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 International Journal of Differential Equations |
| title | Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities |
| title_full | Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities |
| title_fullStr | Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities |
| title_full_unstemmed | Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities |
| title_short | Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities |
| title_sort | well posedness and numerical study for solutions of a parabolic equation with variable exponent nonlinearities |
| url | http://dx.doi.org/10.1155/2018/9754567 |
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