Fourier spectral approximation to long-time behavior of three dimensional Ginzburg-Landau type equation*

2006 ◽  
Vol 27 (3) ◽  
pp. 293-318 ◽  
Author(s):  
Shujuan Lü ◽  
Qishao Lu
Keyword(s):  
Three Dimensional ◽  
Type Equation ◽  
Time Behavior ◽  
Spectral Approximation ◽  
Long Time Behavior ◽  
Ginzburg Landau ◽  
Long Time

scholarly journals EXTREME LONG-TIME DYNAMIC MONTE CARLO SIMULATIONS FOR METASTABLE DECAY IN THE d=3 ISING FERROMAGNET

2003 ◽  
Vol 14 (01) ◽  
pp. 121-131 ◽  
Author(s):  
MIROSLAV KOLESIK ◽  
M. A. NOVOTNY ◽  
PER ARNE RIKVOLD
Keyword(s):  
Metastable Phase ◽  
Three Dimensional ◽  
Glauber Dynamics ◽  
Simulation Method ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Time Dynamic ◽  
Dynamic Monte Carlo ◽  
Long Time ◽  
Good Agreement

We study the extreme long-time behavior of the metastable phase of the three-dimensional Ising model with Glauber dynamics in an applied magnetic field and at a temperature below the critical temperature. For these simulations, we use the advanced simulation method of projective dynamics. The algorithm is described in detail, together with its application to the escape from the metastable state. Our results for the field dependence of the metastable lifetime are in good agreement with theoretical expectations and span more than 50 decades in time.

scholarly journals Strong Solutions and Global Attractors for Kirchhoff Type Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Xiangping Chen
Keyword(s):  
Phase Space ◽  
Type Equation ◽  
Strong Solutions ◽  
Global Attractors ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Long Time ◽  
Linear Damping

We study the long-time behavior of the Kirchhoff type equation with linear damping. We prove the existence of strong solution and the semigroup associated with the solution possesses a global attractor in the higher phase space.

scholarly journals Oscillation of three-dimensional time scale systems with fixed point theorems

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1915-1925
Author(s):  
Özkan Öztürk ◽  
Raegan Higgins ◽  
Georgia Kittou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Three Dimensional ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Nonoscillatory Solutions ◽  
Long Time ◽  
Oscillation And Nonoscillation

Oscillation and nonoscillation theories play very important roles in gaining information about the long-time behavior of solutions of a system. Therefore, we investigate the asymptotic behavior of nonoscillatory solutions as well as the existence of such solutions so that one can determine the limit behavior. For the existence, we use some fixed point theorems such as Schauder?s fixed point theorem and the Knaster fixed point theorem.

A Three-Dimensional Autowave Turbulence

1998 ◽  
Vol 08 (04) ◽  
pp. 677-684 ◽  
Author(s):  
V. N. Biktashev
Keyword(s):  
Three Dimensional ◽  
Topological Defects ◽  
Self Organization ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Vortex Filaments ◽  
Principal Role ◽  
Cardiac Fibrillation ◽  
Internal Instability ◽  
Long Time

Autowave vortices are topological defects in autowave fields in nonlinear active media of various natures and serve as centers of self-organization in the medium. In three-dimensional media, the topological defects are lines, called vortex filaments. Evolution of three-dimensional vortices, in certain conditions, can be described in terms of evolution of their filaments, analogously to that of hydrodynamical vortices in LIA approximation. In the motion equation for the filament, a coefficient called filament tension, plays a principal role, and determines qualitative long-time behavior. While vortices with positive tension tend to shrink and so either collapse or stabilize to a straight shape, depending on boundary conditions, vortices with negative tension show internal instability of shape. This is an essentially three-dimensional effect, as two-dimensional media with the same parameters do not possess any peculiar properties. In large volumes, the instability of filaments can lead to propagating, nondecremental activity composed of curved vortex filaments that multiply and annihilate in an apparently chaotic manner. This may be related to a mechanism of cardiac fibrillation.

scholarly journals Long time behavior of the Ginzburg-Landau superconductivity equations

1995 ◽  
Vol 8 (2) ◽  
pp. 31-34 ◽  
Author(s):  
Q. Tang ◽  
S. Wang
Keyword(s):  
Time Behavior ◽  
Long Time Behavior ◽  
Ginzburg Landau ◽  
Long Time

scholarly journals Long-time behavior of Ginzburg-Landau systems far from equilibrium

1981 ◽  
Vol 24 (5) ◽  
pp. 2592-2602 ◽  
Author(s):  
E. Coutsias ◽  
B. A. Huberman
Keyword(s):  
Time Behavior ◽  
Long Time Behavior ◽  
Ginzburg Landau ◽  
Long Time ◽  
Far From Equilibrium

scholarly journals Well-posedness and long time behavior of an Allen-Cahn type equation

2013 ◽  
Vol 12 (6) ◽  
pp. 2811-2827 ◽  
Author(s):  
Haydi Israel ◽  
Keyword(s):  
Type Equation ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time
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