Energy decay of nonlocal viscoelastic equations with nonlinear damping and polynomial nonlinearity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914176552665088 |
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| author | Peng, Qingqing Liu, Yikan |
| author_facet | Peng, Qingqing Liu, Yikan |
| contents | This paper is concerned with the energy decay of a viscoelastic variable coefficient wave equation with nonlocality in time as well as nonlinear damping and polynomial nonlinear terms. Using the Lyapunov method, we establish a polynomial energy decay for the solution under relatively weak assumptions regarding the kernel of the nonlocal term. More specifically, we improve the decay rate of the energy by additionally imposing a certain convexity assumption on the kernel. Several examples are provided to confirm such improvements to faster polynomial or even exponential decays. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07350 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Energy decay of nonlocal viscoelastic equations with nonlinear damping and polynomial nonlinearity Peng, Qingqing Liu, Yikan Analysis of PDEs 35L20, 35L70, 35B40 This paper is concerned with the energy decay of a viscoelastic variable coefficient wave equation with nonlocality in time as well as nonlinear damping and polynomial nonlinear terms. Using the Lyapunov method, we establish a polynomial energy decay for the solution under relatively weak assumptions regarding the kernel of the nonlocal term. More specifically, we improve the decay rate of the energy by additionally imposing a certain convexity assumption on the kernel. Several examples are provided to confirm such improvements to faster polynomial or even exponential decays. |
| title | Energy decay of nonlocal viscoelastic equations with nonlinear damping and polynomial nonlinearity |
| topic | Analysis of PDEs 35L20, 35L70, 35B40 |
| url | https://arxiv.org/abs/2503.07350 |