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.

scholarly journals Long-Time Behavior of First-Order Mean Field Games on Euclidean Space

2019 ◽  
Vol 10 (2) ◽  
pp. 361-390
Author(s):  
Piermarco Cannarsa ◽  
Wei Cheng ◽  
Cristian Mendico ◽  
Kaizhi Wang
Keyword(s):  
Euclidean Space ◽  
Mean Field ◽  
Mean Field Games ◽  
Time Behavior ◽  
Long Time Behavior ◽  
First Order ◽  
Long Time

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 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 On the Convergence of Bounded Solutions of Non Homogeneous Gradient-like Systems

2017 ◽  
Vol 1 (1) ◽  
pp. 61
Author(s):  
Phuong Minh Tran ◽  
Nhan Thanh Nguyen
Keyword(s):  
Lyapunov Function ◽  
Accumulation Point ◽  
Convergence Result ◽  
Time Behavior ◽  
Bounded Solutions ◽  
Creative Commons ◽  
Angle Condition ◽  
Łojasiewicz Inequality ◽  
Long Time ◽  
Lojasiewicz Inequality

We study the long time behavior of the bounded solutions of non homogeneous gradient-like system which admits a strict Lyapunov function. More precisely, we show that any bounded solution of the gradient-like system converges to an accumulation point as time goes to infinity under some mild hypotheses. As in homogeneous case, the key assumptions for this system are also the angle condition and the Kurdyka-Lojasiewicz inequality. The convergence result will be proved under a L1 -condition of the perturbation term. Moreover, if the Lyapunov function satisfies a Lojasiewicz inequality then the rate of convergence will be even obtained.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.

scholarly journals Asymptotic limits for a nonlinear integro-differential equation modelling leukocytes’ rolling on arterial walls

Nonlinearity ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 843-869
Author(s):  
Vuk Milišić ◽  
Christian Schmeiser
Keyword(s):  
Mathematical Framework ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Asymptotic Results ◽  
Differential Model ◽  
Absolute Value ◽  
Arterial Walls ◽  
Equation Modelling ◽  
Convergence Results ◽  
Long Time

Abstract We consider a nonlinear integro-differential model describing z, the position of the cell center on the real line presented in Grec et al (2018 J. Theor. Biol. 452 35–46). We introduce a new ɛ-scaling and we prove rigorously the asymptotics when ɛ goes to zero. We show that this scaling characterizes the long-time behavior of the solutions of our problem in the cinematic regime (i.e. the velocity z ˙ tends to a limit). The convergence results are first given when ψ, the elastic energy associated to linkages, is convex and regular (the second order derivative of ψ is bounded). In the absence of blood flow, when ψ, is quadratic, we compute the final position z ∞ to which we prove that z tends. We then build a rigorous mathematical framework for ψ being convex but only Lipschitz. We extend convergence results with respect to ɛ to the case when ψ′ admits a finite number of jumps. In the last part, we show that in the constant force case [see model 3 in Grec et al (2018 J. Theor. Biol. 452 35–46), i.e. ψ is the absolute value)] we solve explicitly the problem and recover the above asymptotic results.

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.

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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