# Global Existence for a Nonstandard Viscous Cahn-Hilliard System with Dynamic Boundary Condition

@article{Colli2017GlobalEF, title={Global Existence for a Nonstandard Viscous Cahn-Hilliard System with Dynamic Boundary Condition}, author={Pierluigi Colli and Gianni Gilardi and J{\"u}rgen Sprekels}, journal={SIAM J. Math. Anal.}, year={2017}, volume={49}, pages={1732-1760} }

In this paper, we study a model for phase segregation taking place in a spatial domain that was introduced by Podio-Guidugli [Ric. Mat., 55 (2006), pp. 105--118]. The model consists of a strongly coupled system of nonlinear parabolic differential equations, in which products between the unknown functions and their time derivatives occur, that are difficult to handle analytically. In contrast to the existing literature about this PDE system, we consider here a dynamic boundary condition…

## 10 Citations

Limiting Problems for a Nonstandard Viscous Cahn–Hilliard System with Dynamic Boundary Conditions

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This note is concerned with a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by boundary and initial conditions.…

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Optimal boundary control of a nonstandard Cahn-Hilliard system with dynamic boundary condition and double obstacle inclusions

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In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006), pp.…

The Cahn-Hilliard Equation with Forward-Backward Dynamic Boundary Condition via Vanishing Viscosity

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An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn–Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to…

Asymptotic limits and optimal control for the Cahn–Hilliard system with convection and dynamic boundary conditions

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A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions

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The Cahn–Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to many different contexts in several…

NSF–CBMS CONFERENCE ON THE CAHN–HILLIARD EQUATION: RECENT ADVANCES AND APPLICATIONS PRELIMINARY READING

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which is precisely the equation known as the Cahn–Hilliard equation, was proposed by J.W. Cahn and J.E. Hilliard in 1958 (see [63]). These equations play an essential role in materials science as…

The Cahn–Hilliard equation and some of its variants

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Our aim in this article is to review and discuss the Cahn–Hilliard equation, as well as someof its variants. Such variants have applications in, e.g., biology and image inpainting.

An Allen–Cahn equation based on an unconstrained order parameter and its Cahn–Hilliard limit

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Vanishing diffusion in a dynamic boundary condition for the Cahn–Hilliard equation

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The initial boundary value problem for a Cahn-Hilliard system subject to a dynamic boundary condition of Allen-Cahn type is treated. The vanishing of the surface diffusion on the dynamic boundary…

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