On the existence, uniqueness and regularity of solutions to the phase-field system with a general regular potential and a general class of nonlinear and non-homogeneous boundary conditions

DOI10.1016/j.na.2014.10.003zbMath1304.35167OpenAlexW2040165473MaRDI QIDQ478297

Costică Moroşanu, Alain Miranville, Ovidiu Cârjǎ

Publication date: 3 December 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2014.10.003

zbMATH Keywords

phase-field modelsAllen-Cahn equationnonlinear parabolic systemsLeray-Schauder principledynamic boundary conditions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Thermodynamics in solid mechanics (74A15) Stefan problems, phase changes, etc. (80A22) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Ginzburg-Landau equations (35Q56)

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Cites Work

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• Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions
• Some questions in the optimal control of distributed systems
• Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
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