A One-Dimensional Time-Fractional Damped Wave Equation with a Convection Term
We investigate a semilinear time-fractional damped wave equation in one dimension, posed in a bounded interval. The considered equation involves a convection term and singular potentials on one extremity of the interval. A Dirichlet boundary condition depending on the time-variable is imposed. Using...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/5/1071 |
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| author | Ibtisam Aldawish Mohamed Jleli Bessem Samet |
| author_facet | Ibtisam Aldawish Mohamed Jleli Bessem Samet |
| author_sort | Ibtisam Aldawish |
| collection | DOAJ |
| description | We investigate a semilinear time-fractional damped wave equation in one dimension, posed in a bounded interval. The considered equation involves a convection term and singular potentials on one extremity of the interval. A Dirichlet boundary condition depending on the time-variable is imposed. Using nonlinear capacity estimates, we establish sufficient conditions for the nonexistence of weak solutions to the considered problem. In particular, when the boundary condition is independent of time, we show the existence of a Fujita-type critical exponent. |
| first_indexed | 2024-03-11T03:16:56Z |
| format | Article |
| id | doaj.art-e0656acc661e474e8e474879f47dfb51 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T03:16:56Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e0656acc661e474e8e474879f47dfb512023-11-18T03:30:32ZengMDPI AGSymmetry2073-89942023-05-01155107110.3390/sym15051071A One-Dimensional Time-Fractional Damped Wave Equation with a Convection TermIbtisam Aldawish0Mohamed Jleli1Bessem Samet2Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaWe investigate a semilinear time-fractional damped wave equation in one dimension, posed in a bounded interval. The considered equation involves a convection term and singular potentials on one extremity of the interval. A Dirichlet boundary condition depending on the time-variable is imposed. Using nonlinear capacity estimates, we establish sufficient conditions for the nonexistence of weak solutions to the considered problem. In particular, when the boundary condition is independent of time, we show the existence of a Fujita-type critical exponent.https://www.mdpi.com/2073-8994/15/5/1071damped wave equationCaputo fractional derivativeconvection termnonexistence |
| spellingShingle | Ibtisam Aldawish Mohamed Jleli Bessem Samet A One-Dimensional Time-Fractional Damped Wave Equation with a Convection Term Symmetry damped wave equation Caputo fractional derivative convection term nonexistence |
| title | A One-Dimensional Time-Fractional Damped Wave Equation with a Convection Term |
| title_full | A One-Dimensional Time-Fractional Damped Wave Equation with a Convection Term |
| title_fullStr | A One-Dimensional Time-Fractional Damped Wave Equation with a Convection Term |
| title_full_unstemmed | A One-Dimensional Time-Fractional Damped Wave Equation with a Convection Term |
| title_short | A One-Dimensional Time-Fractional Damped Wave Equation with a Convection Term |
| title_sort | one dimensional time fractional damped wave equation with a convection term |
| topic | damped wave equation Caputo fractional derivative convection term nonexistence |
| url | https://www.mdpi.com/2073-8994/15/5/1071 |
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