Pullback attractors for nonclassical diffusion equations with a delay operator
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913611462475776 |
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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 consider the asymptotic behavior of weak solutions for nonclassical non-autonomous diffusion equations with a delay operator in time-dependent spaces when the nonlinear function $g$ satisfies subcritical exponent growth conditions, the delay operator $φ(t, u_t)$ contains some hereditary characteristics and the external force $k \in L_{l o c}^{2}\left(\mathbb{R} ; L^{2}(Ω)\right)$. First, we prove the well-posedness of solutions by using the Faedo-Galerkin approximation method. Then after a series of elaborate energy estimates and calculations, we establish the existence and regularity of pullback attractors in time-dependent spaces $C_{\mathcal{H}_{t}(Ω)}$ and $C_{\mathcal{H}^{1}_{t}(Ω)}$, respectively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_10479 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pullback attractors for nonclassical diffusion equations with a delay operator Yang, Bin Qin, Yuming Miranville, Alain Wang, Ke Analysis of PDEs Dynamical Systems 35B40, 35B41, 35B65, 35K57 In this paper, we consider the asymptotic behavior of weak solutions for nonclassical non-autonomous diffusion equations with a delay operator in time-dependent spaces when the nonlinear function $g$ satisfies subcritical exponent growth conditions, the delay operator $φ(t, u_t)$ contains some hereditary characteristics and the external force $k \in L_{l o c}^{2}\left(\mathbb{R} ; L^{2}(Ω)\right)$. First, we prove the well-posedness of solutions by using the Faedo-Galerkin approximation method. Then after a series of elaborate energy estimates and calculations, we establish the existence and regularity of pullback attractors in time-dependent spaces $C_{\mathcal{H}_{t}(Ω)}$ and $C_{\mathcal{H}^{1}_{t}(Ω)}$, respectively. |
| title | Pullback attractors for nonclassical diffusion equations with a delay operator |
| topic | Analysis of PDEs Dynamical Systems 35B40, 35B41, 35B65, 35K57 |
| url | https://arxiv.org/abs/2412.10479 |