Time-asymptotic convergence rates towards discrete steady states of a nonlocal selection-mutation model

This paper is concerned with large time behavior of solutions to a semi-discrete model involving nonlinear competition that describes the evolution of a trait-structured population. Under some threshold assumptions, the steady solution is shown unique and strictly positive, and also globally stable. The exponential convergence rate to the steady state is also established. These results are consistent with the results in [P.-E. Jabin, H. L. Liu. Nonlinearity 30 (2017) 4220–4238] for the continuous model.

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LARGE-TIME BEHAVIOR OF DISCRETE KINETIC EQUATIONS WITH NON-SYMMETRIC INTERACTIONS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202502002239 ◽

2002 ◽

Vol 12 (11) ◽

pp. 1555-1564 ◽

Cited By ~ 9

Author(s):

ANTON ARNOLD ◽

JOSE A. CARRILLO ◽

MOULAY D. TIDRIRI

Keyword(s):

Steady State ◽

Large Time ◽

Exponential Convergence ◽

Kinetic Equations ◽

Initial Boundary ◽

Initial Boundary Value Problem ◽

Large Time Behavior ◽

Time Behavior ◽

Velocity Models ◽

Initial Boundary Value

We consider the initial-boundary value problem for general linear discrete velocity models appearing in kinetic theory. With time-independent inflow boundary data we prove the existence of a unique steady state and the exponential convergence in time towards the steady state. The proof is based on the construction of suitable multiplyers used in a weighted L2-norm.

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Time-asymptotic convergence rates towards the discrete evolutionary stable distribution

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202515500426 ◽

2015 ◽

Vol 25 (08) ◽

pp. 1589-1616 ◽

Cited By ~ 4

Author(s):

Wenli Cai ◽

Pierre-Emmanuel Jabin ◽

Hailiang Liu

Keyword(s):

Stable Distribution ◽

Convergence Rates ◽

Exponential Convergence ◽

Continuous Model ◽

Asymptotic Convergence ◽

Discrete Dynamics ◽

Differential Model ◽

Continuous Trait ◽

Fully Discrete ◽

Algebraic Convergence

This paper is concerned with the discrete dynamics of an integro-differential model that describes the evolution of a population structured with respect to a continuous trait. Various time-asymptotic convergence rates towards the discrete evolutionary stable distribution (ESD) are established. For some special ESD satisfying a strict sign condition, the exponential convergence rates are obtained for both semi-discrete and fully discrete schemes. Towards the general ESD, the algebraic convergence rate that we find is consistent with the known result for the continuous model.

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Large time behavior of the logistic age-structured population model in a changing environment

Asymptotic Analysis ◽

10.3233/asy-171409 ◽

2017 ◽

Vol 102 (1-2) ◽

pp. 21-54 ◽

Cited By ~ 1

Author(s):

Vladimir Kozlov ◽

Sonja Radosavljevic ◽

Uno Wennergren

Keyword(s):

Population Model ◽

Large Time ◽

Large Time Behavior ◽

Time Behavior ◽

Changing Environment ◽

Structured Population Model ◽

Structured Population ◽

Age Structured ◽

Age Structured Population

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Global well-posedness of the full compressible Hall-MHD equations

Advances in Nonlinear Analysis ◽

10.1515/anona-2020-0178 ◽

2021 ◽

Vol 10 (1) ◽

pp. 1235-1254

Author(s):

Qiang Tao ◽

Canze Zhu

Keyword(s):

Global Solution ◽

Large Time ◽

Initial Temperature ◽

Large Time Behavior ◽

Initial Energy ◽

Mhd Equations ◽

Well Posedness ◽

Time Behavior ◽

Magnetohydrodynamic Flows ◽

Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

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Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation

Georgian Mathematical Journal ◽

10.1515/gmj.2008.531 ◽

2008 ◽

Vol 15 (3) ◽

pp. 531-539

Author(s):

Temur Jangveladze ◽

Zurab Kiguradze

Keyword(s):

Magnetic Field ◽

Differential Equation ◽

Boundary Conditions ◽

Large Time ◽

Dirichlet Boundary ◽

Large Time Behavior ◽

Dirichlet Boundary Conditions ◽

Time Behavior ◽

Integro Differential Equation ◽

Homogeneous Data

Abstract Large time behavior of solutions to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. The rate of convergence is given, too. Dirichlet boundary conditions with homogeneous data are considered.

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