Maximal attractor for the system of a Landau-Ginzburg theory for structural phase transitions in shape memory alloys

DOI10.1016/S0167-2789(98)00167-5zbMath0944.35104OpenAlexW2095445455MaRDI QIDQ1808331

Songmu Zheng, Juergen Sprekels

Publication date: 6 December 1999

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(98)00167-5

zbMATH Keywords

orbitsnonlinear thermoviscoelasticitymartensitic phase transitionscompact attractorLandau-Ginzburg theoryshape memory allows

Mathematics Subject Classification ID

Related Items (11)

Long-time dynamics of \(N\)-dimensional structure equations with thermal memory ⋮ Maximal attractor for the coupled Cahn-Hilliard equations ⋮ Global attractor for thermoelasticity in shape memory alloys without viscosity ⋮ Global attractor for the Ginzburg-Landau thermoviscoelastic systems with hinged boundary conditions ⋮ Exponential stability and universal attractors for the Navier-Stokes equations of compressible fluids between two horizontal parallel plates in \({\mathbb R}^3\) ⋮ Well-posedness for solid-liquid phase transitions with a fourth-order nonlinearity ⋮ Global attractor for a nonlinear viscoelastic model ⋮ Global existence and asymptotic behavior for a viscous, heat-conductive, one-dimensinal real gas with fixed and thermally insulated endpoints ⋮ Universal attractor in \(H^4\) for the nonlinear one-dimensional compressible Navier-Stokes equations ⋮ Global attractor for a nonlinear thermoviscoelastic model with a non-convex free energy density ⋮ Exponential stability for a nonlinear one-dimensional heat-conductive viscous real gas

Cites Work

• Unnamed Item
• Global existence and asymptotic behavior in nonlinear thermoviscoelasticity
• Global solutions to the equations of a Ginzburg-Landau theory for structural phase transitions in shape memory alloys
• Phase transitions in one-dimensional nonlinear viscoelasticity: Admissibility and stability
• Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity
• On a one-dimensional nonlinear thermoviscoelastic model for structural phase transitions in shape memory alloys
• Infinite-dimensional dynamical systems in mechanics and physics.
• Hysteresis and phase transitions
• Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys
• Global Smooth Solutions to the Initial-Boundary Value Problem for the Equations of One-Dimensional Nonlinear Thermoviscoelasticity
• Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity
• Creep and yield in martensitic transformations
• Existence of solutions to some non-linear thermoelastic systems with viscosity
• On The Coupled Cahn-hilliard Equations
• Global large solutions to initial-boundary value problems in one-dimensional nonlinear thermoviscoelasticity
• A nonlinear boundary value problem involving a nonlocal term
• Asymptotic Behavior of the Solutions to a Landau--Ginzburg System with Viscosity for Martensitic Phase Transitions in Shape Memory Alloys
• Global existence and asymptotic behavior of weak solutions to nonlinear thermoviscoelastic systems with clamped boundary conditions
• The Penrose–Fife-type equations: counting the one-dimensional stationary solutions
• On the existence of solutions to the equation \(u_{tt}=u_{xxt}+\sigma (u_x)_x\)

This page was built for publication: Maximal attractor for the system of a Landau-Ginzburg theory for structural phase transitions in shape memory alloys