Existence and upper semicontinuity of pullback attractors for Kirchhoff wave equations in time-dependent spaces
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917595681128448 |
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| author | Yang, Bin Qin, Yuming Miranville, Alain Wang, Ke |
| author_facet | Yang, Bin Qin, Yuming Miranville, Alain Wang, Ke |
| contents | In this paper, we shall investigate the existence and upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations with a strong damping in the time-dependent space $X_t$. After deriving the existence and uniqueness of solutions by the Faedo-Galerkin approximation method, we establish the existence of pullback attractors. Later on, we prove the upper semicontinuity of pullback attractors between the Kirchhoff-type wave equations with $δ\geq 0$ and the conventional wave equations with $δ=0$ by a series of complex energy estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14479 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and upper semicontinuity of pullback attractors for Kirchhoff wave equations in time-dependent spaces Yang, Bin Qin, Yuming Miranville, Alain Wang, Ke Analysis of PDEs Dynamical Systems 35B40, 35B41, 35L05 In this paper, we shall investigate the existence and upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations with a strong damping in the time-dependent space $X_t$. After deriving the existence and uniqueness of solutions by the Faedo-Galerkin approximation method, we establish the existence of pullback attractors. Later on, we prove the upper semicontinuity of pullback attractors between the Kirchhoff-type wave equations with $δ\geq 0$ and the conventional wave equations with $δ=0$ by a series of complex energy estimates. |
| title | Existence and upper semicontinuity of pullback attractors for Kirchhoff wave equations in time-dependent spaces |
| topic | Analysis of PDEs Dynamical Systems 35B40, 35B41, 35L05 |
| url | https://arxiv.org/abs/2402.14479 |