Knopf, Patrik and Stange, Jonas (2024) Well-posedness of a bulk-surface convective Cahn-Hilliard system with dynamic boundary conditions. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 31 (5): 82. ISSN 1021-9722, 1420-9004
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We consider a general class of bulk-surface convective Cahn-Hilliard systems with dynamic boundary conditions. In contrast to classical Neumann boundary conditions, the dynamic boundary conditions of Cahn-Hilliard type allow for dynamic changes of the contact angle between the diffuse interface and the boundary, a convection-induced motion of the contact line as well as absorption of material by the boundary. The coupling conditions for bulk and surface quantities involve parameters K , L is an element of [ 0 , infinity ] \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K,L\in [0,\infty ]$$\end{document} , whose choice declares whether these conditions are of Dirichlet, Robin or Neumann type. We first prove the existence of a weak solution to our model in the case K , L is an element of ( 0 , infinity ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K,L\in (0,\infty )$$\end{document} by means of a Faedo-Galerkin approach. For all other cases, the existence of a weak solution is then shown by means of the asymptotic limits, where K and L are sent to zero or to infinity, respectively. Eventually, we establish higher regularity for the phase-fields, and we prove the uniqueness of weak solutions given that the mobility functions are constant.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | EQUATION; CONVERGENCE; MODEL; Convective Cahn-Hilliard equation; Bulk-surface interaction; Dynamic boundary conditions; Dynamic contact angle; Moving contact line |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 23 Jul 2025 05:00 |
| Last Modified: | 23 Jul 2025 05:00 |
| URI: | https://pred.uni-regensburg.de/id/eprint/63477 |
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