Well-posedness and global attractor for wave equation with displacement dependent damping and super-cubic nonlinearity
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| Format: | Preprint |
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2025
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| _version_ | 1866916732512239616 |
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| author | Liu, Cuncai Meng, Fengjuan Zhang, Chang |
| author_facet | Liu, Cuncai Meng, Fengjuan Zhang, Chang |
| contents | This work investigates the semilinear wave equation featuring the displacement dependent term $σ(u)\partial_t u $ and nonlinearity $f(u)$. By developing refined space-time a priori estimates under extended ranges of the nonlinearity exponents with $σ(u)$ and $f(u)$, the well-posedness of the weak solution is established. Furthermore, the existence of a global attractor in the naturally phase space $H^1_0(Ω)\times L^2(Ω)$ is obtained. Moreover, the regularity of the global attractor is established, implying that it is a bounded subset of $(H^2(Ω)\cap H^1_0(Ω))\times H^1_0(Ω)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_07255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness and global attractor for wave equation with displacement dependent damping and super-cubic nonlinearity Liu, Cuncai Meng, Fengjuan Zhang, Chang Analysis of PDEs Dynamical Systems This work investigates the semilinear wave equation featuring the displacement dependent term $σ(u)\partial_t u $ and nonlinearity $f(u)$. By developing refined space-time a priori estimates under extended ranges of the nonlinearity exponents with $σ(u)$ and $f(u)$, the well-posedness of the weak solution is established. Furthermore, the existence of a global attractor in the naturally phase space $H^1_0(Ω)\times L^2(Ω)$ is obtained. Moreover, the regularity of the global attractor is established, implying that it is a bounded subset of $(H^2(Ω)\cap H^1_0(Ω))\times H^1_0(Ω)$. |
| title | Well-posedness and global attractor for wave equation with displacement dependent damping and super-cubic nonlinearity |
| topic | Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2505.07255 |