| Autor: |
Mohammad M. Al-Gharabli, Adel M. Al-Mahdi, Mohammad Kafini |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 6, Iss 9, Pp 10105-10129 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2021587?viewType=HTML |
| Popis: |
In this paper, we consider the following viscoelastic problem with variable exponent and logarithmic nonlinearities: $ u_{tt}-\Delta u+u+ \int_0^tb(t-s)\Delta u(s)ds+|u_t|^{{\gamma}(\cdot)-2}u_t = u\ln{\vert u\vert^{\alpha}}, $ where $ {\gamma}(.) $ is a function satisfying some conditions. We first prove a global existence result using the well-depth method and then establish explicit and general decay results under a wide class of relaxation functions and some specific conditions on the variable exponent function. Our results extend and generalize many earlier results in the literature. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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