Hyperbolic relaxation of the chemical potential in the viscous Cahn-Hilliard equation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929539840475136 |
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| author | Colli, Pierluigi Sprekels, Jürgen |
| author_facet | Colli, Pierluigi Sprekels, Jürgen |
| contents | In this paper, we study a hyperbolic relaxation of the viscous Cahn--Hilliard system with zero Neumann boundary conditions. In fact, we consider a relaxation term involving the second time derivative of the chemical potential in the first equation of the system. We develop a well-posedness, continuous dependence and regularity theory for the initial-boundary value problem. Moreover, we investigate the asymptotic behavior of the system as the relaxation parameter tends to 0 and prove the convergence to the viscous Cahn--Hilliard system. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_16332 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperbolic relaxation of the chemical potential in the viscous Cahn-Hilliard equation Colli, Pierluigi Sprekels, Jürgen Analysis of PDEs 35M33, 35M87, 35B40, 37D35 In this paper, we study a hyperbolic relaxation of the viscous Cahn--Hilliard system with zero Neumann boundary conditions. In fact, we consider a relaxation term involving the second time derivative of the chemical potential in the first equation of the system. We develop a well-posedness, continuous dependence and regularity theory for the initial-boundary value problem. Moreover, we investigate the asymptotic behavior of the system as the relaxation parameter tends to 0 and prove the convergence to the viscous Cahn--Hilliard system. |
| title | Hyperbolic relaxation of the chemical potential in the viscous Cahn-Hilliard equation |
| topic | Analysis of PDEs 35M33, 35M87, 35B40, 37D35 |
| url | https://arxiv.org/abs/2408.16332 |