Existence and uniqueness of solutions to singular Cahn-Hilliard equations with nonlinear viscosity terms and dynamic boundary conditions
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Publication:6297483
DOI10.1016/J.JMAA.2018.09.034arXiv1802.02877WikidataQ129206004 ScholiaQ129206004MaRDI QIDQ6297483
Publication date: 8 February 2018
Abstract: We prove global existence and uniqueness of solutions to a Cahn-Hilliard system with nonlinear viscosity terms and nonlinear dynamic boundary conditions. The problem is highly nonlinear, characterized by four nonlinearities and two separate diffusive terms, all acting in the interior of the domain or on its boundary. Through a suitable approximation of the problem based on abstract theory of doubly nonlinear evolution equations, existence and uniqueness of solutions are proved using compactness and monotonicity arguments. The asymptotic behaviour of the solutions as the the diffusion operator on the boundary vanishes is also shown.
Initial-boundary value problems for higher-order parabolic equations (35K35) Semilinear parabolic equations (35K58)
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