Existence and uniqueness of solutions to singular Cahn-Hilliard equations with nonlinear viscosity terms and dynamic boundary conditions

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.

Key words and phrases: Cahn-Hilliard system, dynamic boundary conditions, nonlinear viscosity, existence of solutions, uniqueness

References in corpus (3)

• From the viscous Cahn-Hilliard equation to a regularized forward-backward parabolic equation
• A doubly nonlinear Cahn-Hilliard system with nonlinear viscosity
• Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials

Cited by in corpus (8)

• Nonlocal-to-local convergence of Cahn-Hilliard equations: Neumann boundary conditions and viscosity terms
• Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics
• The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit
• Optimal distributed control of a stochastic Cahn-Hilliard equation
• Bounded solutions and their asymptotics for a doubly nonlinear Cahn-Hilliard system
• Analysis and optimal velocity control of a stochastic convective Cahn-Hilliard equation
• The stochastic Cahn-Hilliard equation with degenerate mobility and logarithmic potential
• Vanishing diffusion in a dynamic boundary condition for the Cahn-Hilliard equation