Energy decay of a viscoelastic wave equation with variable exponent logarithmic nonlinearity and weak damping
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911353700089856 |
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| author | Peng, Qingqing Liu, Yikan |
| author_facet | Peng, Qingqing Liu, Yikan |
| contents | In this paper, we investigate the energy decay of the solution to a viscoelastic wave equation with variable exponents logarithmic nonlinearity and weak damping in a bounded domain. We establish an explicit general decay result under mild conditions on the relaxation function $g$. Furthermore, under the general assumption $g'(t)\leq-ζ(t)G(g(t))$ with some suitably given $ζ$ and $G$, we derive a refined decay estimate improving existing results. In particular, uniform exponential and polynomial decay rates are obtained under a further special situation $g'(t)\leq-ξ(t)g^q(t)$ with $1\leq q<2$, extending earlier studies that were restricted to the case $1\leq q<\frac{3}{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01752 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Energy decay of a viscoelastic wave equation with variable exponent logarithmic nonlinearity and weak damping Peng, Qingqing Liu, Yikan Analysis of PDEs 35L70, 35B40 In this paper, we investigate the energy decay of the solution to a viscoelastic wave equation with variable exponents logarithmic nonlinearity and weak damping in a bounded domain. We establish an explicit general decay result under mild conditions on the relaxation function $g$. Furthermore, under the general assumption $g'(t)\leq-ζ(t)G(g(t))$ with some suitably given $ζ$ and $G$, we derive a refined decay estimate improving existing results. In particular, uniform exponential and polynomial decay rates are obtained under a further special situation $g'(t)\leq-ξ(t)g^q(t)$ with $1\leq q<2$, extending earlier studies that were restricted to the case $1\leq q<\frac{3}{2}$. |
| title | Energy decay of a viscoelastic wave equation with variable exponent logarithmic nonlinearity and weak damping |
| topic | Analysis of PDEs 35L70, 35B40 |
| url | https://arxiv.org/abs/2601.01752 |