On the nonconserved Caginalp phase-field system based on the Maxwell-Cattaneo law with two temperatures and logarithmic potentials

DOI10.3934/dcdsb.2019019zbMath1409.35109OpenAlexW2907621570MaRDI QIDQ1733209

Georges Sadaka, Alain Miranville, Ahmad Makki

Publication date: 21 March 2019

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2019019

zbMATH Keywords

dissipativitywell-posednessglobal attractorsimulationslogarithmic nonlinear termsCaginalp systemMaxwell-Cattaneo lawtwo temperatures

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15) Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer (80M10) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (2)

A splitting method for the Allen-Cahn/Cahn-Hilliard system coupled with heat equation based on Maxwell-Cattaneo law ⋮ On the conserved Caginalp phase-field system with logarithmic potentials based on the Maxwell-Cattaneo law with two temperatures

Uses Software

• FreeFem++

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some mathematical models in phase transition
• A phase-field model based on a three-phase-lag heat conduction
• A doubly nonlinear parabolic equation with a singular potential
• The non-isothermal Allen-Cahn equation with dynamic boundary conditions
• The Caginalp phase-field system with coupled dynamic boundary conditions and singular potentials
• On the Caginalp system with dynamic boundary conditions and singular potentials.
• A generalization of the Caginalp phase-field system based on the Cattaneo law
• An analysis of a phase field model of a free boundary
• Existence of a universal attractor for a fully hyperbolic phase-field system
• Hysteresis and phase transitions
• A type III phase-field system with a logarithmic potential
• Convergence to equilibrium for a parabolic-hyperbolic phase field model with Cattaneo heat flux law
• Long time behavior of solutions to the Caginalp system with singular potential
• On a theory of heat conduction involving two temperature
• On the thermodynamics of non-simple elastic materials with two temperatures
• Asymptotic behavior of solutions to the phase-field equations with Neumann boundary condi\-tions
• Long-time convergence of solutions to a phase-field system
• A Caginalp phase-field system based on type III heat conduction with two temperatures
• On the Caginalp phase-field systems with two temperatures and the Maxwell-Cattaneo law
• A re-examination of the basic postulates of thermomechanics
• Some generalizations of the Caginalp phase-field system
• Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions
• Convergence to equilibrium for a fully hyperbolic phase‐field model with Cattaneo heat flux law
• Finite dimensional exponential attractor for the phase field model
• Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions
• Solution of 2D Boussinesq systems with freefem++: the flat bottom case
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• A generalization of the Allen-Cahn equation
• Theory of two-temperature-generalized thermoelasticity
• Well‐posedness and long time behavior of a parabolic‐hyperbolic phase‐field system with singular potentials
• Long-time stabilization of solutions to a phase-field model with memory

This page was built for publication: On the nonconserved Caginalp phase-field system based on the Maxwell-Cattaneo law with two temperatures and logarithmic potentials