A mathematical analysis of a nonisothermal Allen-Cahn type system

DOI10.1002/mma.2504zbMath1250.35120OpenAlexW2151258678MaRDI QIDQ2912305

Cristina L. D. Vaz, José Luiz Boldrini

Publication date: 14 September 2012

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.2504

zbMATH Keywords

maximum principlephase transitionssolidificationdegree theorybinary alloyphase fieldsemidiscrete spectral Galerkin method

Mathematics Subject Classification ID

Stefan problems, phase changes, etc. (80A22) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (2)

Well-posedness for a phase-field transition system endowed with a polynomial nonlinearity and a general class of nonlinear dynamic boundary conditions ⋮ A qualitative analysis of a second-order anisotropic phase-field transition system endowed with a general class of nonlinear dynamic boundary conditions

Cites Work

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• Asymptotic behaviour of a phase-field model with three coupled equations without uniqueness
• Analysis of a two-phase field model for the solidification of an alloy
• Geometric theory of semilinear parabolic equations
• A generalized phase-field system
• Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
• Modeling melt convection in phase-field simulations of solidification
• Convergence to equilibrium for a parabolic-hyperbolic phase field model with Cattaneo heat flux law
• Existence of solutions to a phase-field model for the isothermal solidification process of a binary alloy

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