Asymptotic behaviour of a phase-field model with three coupled equations without uniqueness

DOI10.1016/j.jde.2009.01.021zbMath1178.35073OpenAlexW2057022906MaRDI QIDQ1022942

Gabriela Planas, Pedro Marín-Rubio, José Real

Publication date: 10 June 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://idus.us.es/xmlui/handle/11441/25949

zbMATH Keywords

multivalued dynamical systemsystem of three equationsfamilies of global attractors

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Nonlinear parabolic equations (35K55) Stefan problems, phase changes, etc. (80A22) Degenerate parabolic equations (35K65) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30)

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Cites Work

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• An analysis of a phase field model of a free boundary
• On attractors of multivalued semi-flows and differential inclusions
• Infinite-dimensional dynamical systems in mechanics and physics.
• Weak solution to some Penrose-Fife phase-field systems with temperature-dependent memory
• Abstract approach to evolution equations of phase-field type and applications
• Asymptotic behavior of solutions to the phase-field equations with Neumann boundary condi\-tions
• Attractors for reaction-diffusion equations: existence and estimate of their dimension
• Finite dimensional exponential attractor for the phase field model
• Weak solutions to a phase-field model with non-constant thermal conductivity
• Attractors of Multivalued Dynamical Processes Generated by Phase-Field Equations
• Weak solutions of a phase-field model for phase change of an alloy with thermal properties
• Long-time behaviour for a model of phase-field type
• Asymptotic behaviour for a phase-field system with hysteresis
• Dynamics of evolutionary equations