A PHASE FIELD MODEL WITH THERMAL MEMORY GOVERNED BY THE ENTROPY BALANCE

DOI10.1142/S0218202503003033zbMath1053.80009OpenAlexW2023578974MaRDI QIDQ3043594

Elena Bonetti, Pierluigi Colli, Michel Frémond

Publication date: 6 August 2004

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

Full work available at URL: https://doi.org/10.1142/s0218202503003033

zbMATH Keywords

initial-boundary value problemexistence of solutionsentropy balancePhase transitionsnonlinear integro-differential PDE's system

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Integro-partial differential equations (45K05) Stefan problems, phase changes, etc. (80A22) Partial functional-differential equations (35R10) Phase transformations in solids (74N99)

Related Items (17)

Time-discretization and global solution for a doubly nonlinear Volterra equation ⋮ Global solution to a singular integro-differential system related to the entropy balance ⋮ Global existence for a singular phase field system related to a sliding mode control problem ⋮ Well-posedness and longtime behavior for a singular phase field system with perturbed phase dynamics ⋮ Singular limit of an integrodifferential system related to the entropy balance ⋮ A new dual approach for a class of phase transitions with memory: existence and long-time behaviour of solutions ⋮ Well-posedness for solid-liquid phase transitions with a fourth-order nonlinearity ⋮ WELL POSEDNESS FOR A PHASE TRANSITION MODEL IN SUPERCONDUCTIVITY WITH VELOCITY AND MAGNETIC CRITICAL FIELDS ⋮ A first order phase transition with non-constant density ⋮ Global existence for a phase separation system deduced from the entropy balance ⋮ Solid-liquid phase changes with different densities ⋮ Existence and boundedness of solutions for a singular phase field system ⋮ Existence of solutions to a phase transition model with microscopic movements ⋮ A three-dimensional phase transition model in ferromagnetism: Existence and uniqueness ⋮ WELL-POSEDNESS OF A PHASE TRANSITION MODEL WITH THE POSSIBILITY OF VOIDS ⋮ Weak solutions and weak-strong uniqueness for a thermodynamically consistent phase-field model ⋮ Ice-water and liquid-vapor phase transitions by a Ginzburg–Landau model

Cites Work

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• Internal dissipation, relaxation property, and free energy in materials with fading memory
• A general theory of heat conduction with finite wave speeds
• Hyperbolic phase change problems in heat conduction with memory
• Well-posedness and longtime behavior of the phase-field model with memory in a history space setting
• A phase transition model with the entropy balance
• NONLINEAR SYSTEMS DESCRIBING PHASE TRANSITION MODELS COMPATIBLE WITH THERMODYNAMICS
• Heat waves
• Thermodynamics of mixtures and phase field theory
• Global solution to a Frémond model for shape memory alloys with thermal memory

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