Well-posedness and global attractor for wave equation with nonlinear damping and super-cubic nonlinearity
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909490038702080 |
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| author | Liu, Cuncai Meng, Fengjuan Han, Xiaoying Zhang, Chang |
| author_facet | Liu, Cuncai Meng, Fengjuan Han, Xiaoying Zhang, Chang |
| contents | This study investigates a semilinear wave equation characterized by nonlinear damping $g(u_t) $ and nonlinearity $f(u)$. First, the well-posedness of weak solutions across broader exponent ranges for $g$ and $f$ is established, by utilizing a priori space-time estimates. Moreover, the existence of a global attractor in the phase space $H^1_0(Ω)\times L^2(Ω)$ is obtained. Furthermore, it is proved that this global attractor is regular, 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_2308_06208 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Well-posedness and global attractor for wave equation with nonlinear damping and super-cubic nonlinearity Liu, Cuncai Meng, Fengjuan Han, Xiaoying Zhang, Chang Analysis of PDEs Dynamical Systems Primary 35B40, Secondary 35B45, 35L70 This study investigates a semilinear wave equation characterized by nonlinear damping $g(u_t) $ and nonlinearity $f(u)$. First, the well-posedness of weak solutions across broader exponent ranges for $g$ and $f$ is established, by utilizing a priori space-time estimates. Moreover, the existence of a global attractor in the phase space $H^1_0(Ω)\times L^2(Ω)$ is obtained. Furthermore, it is proved that this global attractor is regular, 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 nonlinear damping and super-cubic nonlinearity |
| topic | Analysis of PDEs Dynamical Systems Primary 35B40, Secondary 35B45, 35L70 |
| url | https://arxiv.org/abs/2308.06208 |