Global existence and new decay results of a viscoelastic wave equation with variable exponent and logarithmic nonlinearities
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. W...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2021-07-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://aimspress.com/article/doi/10.3934/math.2021587?viewType=HTML |
| Summary: | 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. |
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| ISSN: | 2473-6988 |