Journal ArticleDOI
Asymptotic behavior of the solutions to a Landau-Ginzburg system with viscosity for martensitic phase transitions in shape memory alloys
TLDR
In this article, the system of partial differential equations governing the dynamics of martensitic phase transitions in shape memory alloys under the presence of a (possibly small) viscous stress is investigated.Abstract:
In this paper, we investigate the system of partial differential equations governing the dynamics of martensitic phase transitions in shape memory alloys under the presence of a (possibly small) viscous stress. The corresponding free energy is assumed in Landau--Ginzburg form and nonconvex as a function of the order parameter. Results concerning the asymptotic behavior of the solution as time tends to infinity are proved, and the compactness of the orbit is shown.read more
Citations
More filters
Journal ArticleDOI
Global existence and asymptotic behavior of weak solutions to nonlinear thermoviscoelastic systems with clamped boundary conditions
TL;DR: In this paper, it is shown that for any initial data of (strain, velocity, absolute temperature) (uo,vo>#o) G L°° x Wq'°°x H1, there is a unique global solution (it, v,6) £ C([0, +oo]; L°) xC(0,+oo); JTo1'00) fl L°
Journal ArticleDOI
Maximal attractor for the system of one-dimensional polytropic viscous ideal gas
Songmu Zheng,Yuming Qin +1 more
TL;DR: In this paper, the dynamics of polytropic viscous ideal gas is investigated and the existence of two maximal (universal) attractors in and is proved for any constants 0i, (h, @3,04,05 satisfying certain conditions, two sequences of closed subspaces H^ C H(i) (i = 1,2) are found.
Journal ArticleDOI
Universal attractor in H 4 for the nonlinear one-dimensional compressible Navier-Stokes equations
Yuming Qin,Yuming Qin +1 more
TL;DR: In this paper, the regularity, exponential stability of solutions and existence of universal attractor in H 4 for a nonlinear one-dimensional compressible Navier-Stokes equations describing a motion of heat-conductive viscous real gas in a bounded domain Ω = ( 0, 1 ) were investigated.
Journal ArticleDOI
Global existence and asymptotic behavior for a viscous, heat-conductive, one-dimensional real gas with fixed and thermally insulated endpoints
Journal ArticleDOI
Maximal attractor for the system of a Landau-Ginzburg theory for structural phase transitions in shape memory alloys
Jürgen Sprekels,Songmu Zheng +1 more
TL;DR: In this paper, a system of nonlinear partial differential equations modeling the dynamics of martensitic phase transitions in shape memory alloys is further investigated, and the existence of a compact maximal attractor is proved.
Related Papers (5)
Global solutions to the equations of a Ginzburg-Landau theory for structural phase transitions in shape memory alloys
Jürgen Sprekels,Songmu Zheng +1 more
Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity
Constantine M. Dafermos,L. Hsiao +1 more