Dynamics of a 3D Benjamin–Bona–Mahony equations with sublinear operator

2020 ◽  
Vol 121 (1) ◽  
pp. 75-100
Author(s):  
Mingxia Zhao ◽  
Xin-Guang Yang ◽  
Xingjie Yan ◽  
Xiaona Cui
Keyword(s):  
Shallow Water ◽  
Energy Equation ◽  
Three Dimensional ◽  
Solution Process ◽  
Sublinear Operator ◽  
Sufficient Condition ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Pullback Attractors ◽  
Long Time

This paper is concerned with the tempered pullback dynamics for a three dimensional Benjamin–Bona–Mahony equations with sublinear operator on bounded domain, which describes the long time behavior for long waves model in shallow water with friction. By virtue of a new retarded Gronwall inequality, and using the energy equation method from J.M. Ball (Disc. Cont. Dyn. Syst. 10 (2004) 31–52) to achieve asymptotic compactness for solution process, the minimal family of pullback attractors has been obtained, which reduces a single trajectory under a sufficient condition.

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 Blow-Up Phenomena and Global Existence to a Weakly Dissipative Shallow Water Equation

2014 ◽  
Vol 12 ◽  
pp. 10-20
Author(s):  
Jiang Bo Zhou ◽  
Jun De Chen ◽  
Wen Bing Zhang
Keyword(s):  
Global Existence ◽  
Shallow Water ◽  
Blow Up ◽  
Shallow Water Equation ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Holm Equation ◽  
Special Cases ◽  
Long Time

We first establish the local well-posedness for a weakly dissipative shallow water equation which includes both the weakly dissipative Camassa-Holm equation and the weakly dissipative Degasperis-Procesi equation as its special cases. Then two blow-up results are derived for certain initial profiles. Finally, We study the long time behavior of the solutions.

scholarly journals Long time behavior for a dissipative shallow water model

2017 ◽  
Vol 34 (3) ◽  
pp. 731-757 ◽  
Author(s):  
V. Sciacca ◽  
M.E. Schonbek ◽  
M. Sammartino
Keyword(s):  
Shallow Water ◽  
Water Model ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Shallow Water Model ◽  
Long Time

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 Approximate Kelvin-Voigt Fluid Driven by an External Force Depending on Velocity with Distributed Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yantao Guo ◽  
Shuilin Cheng ◽  
Yanbin Tang
Keyword(s):  
External Force ◽  
Distributed Delay ◽  
Navier Stokes ◽  
Pullback Attractor ◽  
Sufficient Condition ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Prior Estimate ◽  
Long Time ◽  
Voigt Fluid

We consider the approximate 3D Kelvin-Voigt fluid driven by an external force depending on velocity with distributed delay. We investigate the long time behavior of solutions to Navier-Stokes-Voigt equation with a distributed delay external force depending on the velocity of fluid on a bounded domain. By a prior estimate and a contractive function, we give a sufficient condition for the existence of pullback attractor of NSV equation.

scholarly journals Long-Time Behavior for Three Dimensional Compressible Viscousand Heat-Conductive Gases

2020 ◽  
Vol 22 (3) ◽  
Author(s):  
Xiaoping Zhai ◽  
Zhi-Min Chen
Keyword(s):  
Three Dimensional ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time

On the existence and long-time behavior of solutions to stochastic three-dimensional Navier–Stokes–Voigt equations

Stochastics ◽  
2018 ◽  
Vol 91 (4) ◽  
pp. 485-513
Author(s):  
Cung The Anh ◽  
Nguyen Van Thanh
Keyword(s):  
Three Dimensional ◽  
Navier Stokes ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time

scholarly journals Pullback attractors via quasi-stability for non-autonomous lattice dynamical systems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Radosław Czaja
Keyword(s):  
Dynamical Systems ◽  
Global Attractor ◽  
Exponential Attractor ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Pullback Attractors ◽  
Diffusion Operator ◽  
First Order ◽  
Lattice Dynamical Systems ◽  
Long Time

<p style='text-indent:20px;'>In this paper we study long-time behavior of first-order non-autono-mous lattice dynamical systems in square summable space of double-sided sequences using the cooperation between the discretized diffusion operator and the discretized reaction term. We obtain existence of a pullback global attractor and construct pullback exponential attractor applying the introduced notion of quasi-stability of the corresponding evolution process.</p>

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