scholarly journals ASYMPTOTIC BEHAVIOR TO THE 3-D SCHRÖDINGER/HARTREE–POISSON AND WIGNER–POISSON SYSTEMS

2000 ◽  
Vol 10 (06) ◽  
pp. 923-943 ◽  
Author(s):  
J. L. LÓPEZ ◽  
J. SOLER
Keyword(s):  
Asymptotic Behavior ◽  
Quantum Mechanics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Limit Problems ◽  
Self Consistent ◽  
Linear Limit ◽  
Long Time ◽  
Wigner Representation ◽  
Scaling Group

Using an appropriate scaling group for the 3-D Schrödinger–Poisson equation and the equivalence between the Schrödinger formalism and the Wigner representation of quantum mechanics it is proved that, when time goes to infinity, the limit of the rescaled self-consistent potential can be identified as the Coulomb potential. As a consequence, Schrödinger–Poisson and Wigner–Poisson systems are asymptotically simplified and their long-time behavior is explained through the solutions of the corresponding linear limit problems.

scholarly journals Long Time Behavior of the Solution of the Two-Dimensional Dissipative QGE in Lei–Lin Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Moez Benhamed ◽  
Sahar Mohammad Abusalim
Keyword(s):  
Asymptotic Behavior ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Long Time

In this paper, we study the asymptotic behavior of the two-dimensional quasi-geostrophic equations with subcritical dissipation. More precisely, we establish that θtX1−2α vanishes at infinity.

The asymptotic behavior of a stochastic multigroup SIS model

2018 ◽  
Vol 11 (03) ◽  
pp. 1850037 ◽  
Author(s):  
Chunyan Ji ◽  
Daqing Jiang
Keyword(s):  
Asymptotic Behavior ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Endemic Equilibrium ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Sis Model ◽  
Stochastic Perturbations ◽  
Long Time ◽  
Theoretical Results

In this paper, we explore the long time behavior of a multigroup Susceptible–Infected–Susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.

scholarly journals ASYMPTOTIC BEHAVIOR OF NONLINEAR SCHRÖDINGER SYSTEMS WITH LINEAR COUPLING

2014 ◽  
Vol 11 (01) ◽  
pp. 159-183 ◽  
Author(s):  
PAOLO ANTONELLI ◽  
RADA MARIA WEISHÄUPL
Keyword(s):  
Asymptotic Behavior ◽  
Rabi Frequency ◽  
Original System ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Linear Coupling ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger Systems ◽  
Long Time ◽  
Schrödinger Systems

A system of two coupled nonlinear Schrödinger equations is investigated. In addition, a linear coupling which models an external driven field described by the Rabi frequency is considered. Asymptotics for large Rabi frequency are carried out and the convergence in the appropriate Strichartz space is proven. As a consequence, the global existence for the limiting system yields us a criterion for the long time behavior of the original system.

scholarly journals Asymptotic Behavior of Bounded Solutions to a First Order Gradient-like System

2019 ◽  
Vol 3 (1) ◽  
pp. 312
Author(s):  
Minh-Phuong Tran ◽  
Thanh-Nhan Nguyen
Keyword(s):  
Asymptotic Behavior ◽  
Original Work ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Bounded Solutions ◽  
First Order ◽  
Creative Commons ◽  
Convergence Results ◽  
Long Time ◽  
Open Access Article

In this paper, we prove the long time behavior of bounded solutions to a first order gradient-like system with low damping and perturbation terms. Our convergence results are obtained under some hypotheses of KurdykaLojasiewicz inequality and the angle and comparability condition.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Long-time behavior of solutions for a system of N-coupled nonlinear dissipative half-wave equations

Analysis ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Brahim Alouini
Keyword(s):  
Asymptotic Behavior ◽  
Initial Value Problem ◽  
Wave Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Half Wave ◽  
Long Time ◽  
Asymptotic Dynamics

Abstract In the current paper, we consider a system of N-coupled weakly dissipative fractional nonlinear Schrödinger equations. The well-posedness of the initial value problem is established by a refined analysis based on a limiting argument as well as the study of the asymptotic dynamics of the solutions. This asymptotic behavior is described by the existence of a compact global attractor in the appropriate energy space.

Asymptotic behavior and blowup for two generalized Ginzburg–Landau type equations with several nonlinear source terms

2017 ◽  
Vol 10 (02) ◽  
pp. 1750029
Author(s):  
Shoubo Jin ◽  
Zufeng Zhang ◽  
Qun Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Source Terms ◽  
Ginzburg Landau ◽  
Nonlinear Source ◽  
Blowup Of Solutions ◽  
Long Time ◽  
Time Blowup

In this paper, the long-time behavior and blowup of solutions for two generalized Ginzburg–Landau type equations with several nonlinear source terms are investigated. First, the conditions in which the solutions of the two equations are positive are analyzed by using Green’s function. According to the characteristics of nonlinear terms, four different functionals are constructed for solving the problems. Finally, we obtain the long-time behavior and finite-time blowup of solutions for the initial and boundary value problem by using these functionals.

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

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