On the existence, uniqueness and regularity of solutions to the phase-field transition system with non-homogeneous Cauchy–Neumann and nonlinear dynamic boundary conditions

This paper is devoted to the study of a Caginalp phase-field system endowed with non-homogeneous Cauchy–Neumann and nonlinear dynamic boundary conditions. We first prove the existence, uniqueness and regularity of solutions to an Allen–Cahn equation. Our approach allows to consider in the dynamic bo...

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Bibliographic Details
Published in:Applied mathematical modelling 2016-01, Vol.40 (1), p.192-207
Main Authors: Miranville, Alain, Moroşanu, Costică
Format: Article
Language:English
Subjects:
Dynamic boundary conditions
Leray–Schauder principle
Nemytskij’s operator
Nonlinear parabolic systems
Phase-field models
Thermodynamics
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Summary:This paper is devoted to the study of a Caginalp phase-field system endowed with non-homogeneous Cauchy–Neumann and nonlinear dynamic boundary conditions. We first prove the existence, uniqueness and regularity of solutions to an Allen–Cahn equation. Our approach allows to consider in the dynamic boundary conditions a nonlinearity of higher order than in the known results. The existence, uniqueness and regularity of solutions to the Caginalp system in this new formulation is also proven.
ISSN:0307-904X
DOI:10.1016/j.apm.2015.04.039