Weak solution to some Penrose-Fife phase-field systems with temperature-dependent memory

DOI10.1006/jdeq.1997.3344zbMath0897.45012OpenAlexW2011711739MaRDI QIDQ1382699

Pierluigi Colli, Juergen Sprekels

Publication date: 30 July 1998

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

Full work available at URL: https://doi.org/10.1006/jdeq.1997.3344

zbMATH Keywords

weak solutionexistenceinitial-boundary value problemuniquenessPenrose-Fife phase-field systemssystem of integro-partial differential equations

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Stefan problems, phase changes, etc. (80A22)

Related Items (8)

Local existence of solutions of a three phase‐field model for solidification ⋮ Global weak solutions to an initial-boundary value problem for a three-phase field model of solidification ⋮ ON PHASE–FIELD EQUATIONS OF PENROSE–FIFE TYPE WITH THE NON–CONSERVED ORDER PARAMETER UNDER FLUX BOUNDARY CONDITION. I: GLOBAL–IN–TIME SOLVABILITY ⋮ The conserved Penrose-Fife system with temperature-dependent memory. ⋮ The conserved Penrose-Fife phase field model with special heat flux laws and memory effects ⋮ Three-dimensional solidification with two possible crystallization states: Existence of solutions with flow in the melt ⋮ A PHASE FIELD MODEL WITH THERMAL MEMORY GOVERNED BY THE ENTROPY BALANCE ⋮ Asymptotic behaviour of a phase-field model with three coupled equations without uniqueness

Cites Work

• Thermodynamically consistent models of phase-field type for the kinetics of phase transitions
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• Global smooth solutions to a thermodynamically consistent model of phase- field type in higher space dimensions
• On the relation between the standard phase-field model and a ``thermodynamically consistent phase-field model
• Solutions to a Penrose-Fife model of phase-field type
• Weak solutions to the Penrose-Fife phase field model for a class of admissible heat flux laws
• Global smooth solution to the standard phase-field model with memory
• Well-posedness of the weak formulation for the phase-field model with memory
• Phase transition problems in materials with memory
• Existence and asymptotic results for a system of integro-partial differential equations
• On a Penrose-Fife model with zero interfacial energy leading to a phase-field system of relaxed Stefan type
• A general theory of heat conduction with finite wave speeds
• Heat waves
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