Equation and dynamic boundary condition of Cahn–Hilliard type with singular potentials

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The Cahn-hilliard Equation with Singular Potentials and Dynamic Boundary Conditions

Our aim in this paper is to study the Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. In particular, we prove, owing to proper approximations of the singular potential and a suitable notion of variational solutions, the existence and uniqueness of solutions. We also discuss the separation of the solutions from the singularities of the potential. Finally, we prov...

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Global Solution to the Allen-cahn Equation with Singular Potentials and Dynamic Boundary Conditions

We prove well-posedness results for the solution to an initial and boundaryvalue problem for an Allen-Cahn type equation describing the phenomenon of phase transitions for a material contained in a bounded and regular domain. The dynamic boundary conditions for the order parameter have been recently proposed by some physicists to account for interactions with the walls (see [14] and [20]). We s...

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ژورنال

عنوان ژورنال: Nonlinear Analysis: Theory, Methods & Applications

سال: 2015

ISSN: 0362-546X

DOI: 10.1016/j.na.2015.07.011