Decay result in a problem of a nonlinearly damped wave equation with variable exponent
In this work we study a wave equation with a nonlinear time dependent frictional damping of variable exponent type. The existence and uniqueness results are established using Fadeo-Galerkin approximation method. We also exploit the Komornik lemma to prove the uniform stability result for the energy...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-01-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022170?viewType=HTML |
| _version_ | 1819007756769689600 |
|---|---|
| author | Mohammad Kafini Jamilu Hashim Hassan Mohammad M. Al-Gharabli |
| author_facet | Mohammad Kafini Jamilu Hashim Hassan Mohammad M. Al-Gharabli |
| author_sort | Mohammad Kafini |
| collection | DOAJ |
| description | In this work we study a wave equation with a nonlinear time dependent frictional damping of variable exponent type. The existence and uniqueness results are established using Fadeo-Galerkin approximation method. We also exploit the Komornik lemma to prove the uniform stability result for the energy associated to the solution of the problem under consideration. |
| first_indexed | 2024-12-21T00:29:38Z |
| format | Article |
| id | doaj.art-c5324c507a7c4fa6a4866299098f8b51 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-21T00:29:38Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-c5324c507a7c4fa6a4866299098f8b512022-12-21T19:21:55ZengAIMS PressAIMS Mathematics2473-69882022-01-01723067308210.3934/math.2022170Decay result in a problem of a nonlinearly damped wave equation with variable exponentMohammad Kafini 0Jamilu Hashim Hassan1Mohammad M. Al-Gharabli 21. Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia3. The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia1. Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia2. The Preparatory Year Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 3. The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaIn this work we study a wave equation with a nonlinear time dependent frictional damping of variable exponent type. The existence and uniqueness results are established using Fadeo-Galerkin approximation method. We also exploit the Komornik lemma to prove the uniform stability result for the energy associated to the solution of the problem under consideration.https://www.aimspress.com/article/doi/10.3934/math.2022170?viewType=HTMLviscoelasticityrelaxation functiongeneral decaylogarithmic nonlinearityvariable exponent |
| spellingShingle | Mohammad Kafini Jamilu Hashim Hassan Mohammad M. Al-Gharabli Decay result in a problem of a nonlinearly damped wave equation with variable exponent AIMS Mathematics viscoelasticity relaxation function general decay logarithmic nonlinearity variable exponent |
| title | Decay result in a problem of a nonlinearly damped wave equation with variable exponent |
| title_full | Decay result in a problem of a nonlinearly damped wave equation with variable exponent |
| title_fullStr | Decay result in a problem of a nonlinearly damped wave equation with variable exponent |
| title_full_unstemmed | Decay result in a problem of a nonlinearly damped wave equation with variable exponent |
| title_short | Decay result in a problem of a nonlinearly damped wave equation with variable exponent |
| title_sort | decay result in a problem of a nonlinearly damped wave equation with variable exponent |
| topic | viscoelasticity relaxation function general decay logarithmic nonlinearity variable exponent |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022170?viewType=HTML |
| work_keys_str_mv | AT mohammadkafini decayresultinaproblemofanonlinearlydampedwaveequationwithvariableexponent AT jamiluhashimhassan decayresultinaproblemofanonlinearlydampedwaveequationwithvariableexponent AT mohammadmalgharabli decayresultinaproblemofanonlinearlydampedwaveequationwithvariableexponent |