scholarly journals Global existence and asymptotic behaviour of solutions for a hyperbolic-parabolic model of chemotaxis on network

2021 ◽  
Author(s):  
Yafeng Li ◽  
Chunlai Mu ◽  
Xin Qiao
Keyword(s):  
Global Existence ◽  
Asymptotic Behaviour ◽  
Parabolic System ◽  
Existence And Uniqueness ◽  
System Modeling ◽  
Global Solutions ◽  
Energy Estimates ◽  
Parabolic Model ◽  
Biological Phenomena ◽  
Acyclic Network

In this paper, we discuss a hyperbolic-parabolic system modeling biological phenomena evolving on a network. The global existence of the is obtained by using energy estimates with suitable the transmission conditions at interior. Moreover, for the case of acyclic network, the existence and uniqueness of stationary solution to the system is proposed and it is proved that these ones are asymptotic profiles for a class of global solutions

scholarly journals The asymptotic behaviour of fractional lattice systems with variable delay

2019 ◽  
Vol 22 (3) ◽  
pp. 681-698
Author(s):  
Linfang Liu ◽  
Tomás Caraballo ◽  
Peter E. Kloeden
Keyword(s):  
Asymptotic Behaviour ◽  
Existence And Uniqueness ◽  
Time Delays ◽  
Lipschitz Constant ◽  
Time Derivative ◽  
Global Solutions ◽  
Variable Delay ◽  
Lattice Systems ◽  
Functional Differential ◽  
Fractional Functional

Abstract The existence and uniqueness of global solutions for a fractional functional differential equation is established. The asymptotic behaviour of a lattice system with a fractional substantial time derivative and variable time delays is investigated. The existence of a global attracting set is established. It is shown to be a singleton set under a certain condition on the Lipschitz constant.

Equations de Schrödinger non linéaires en dimension deux

1979 ◽  
Vol 84 (3-4) ◽  
pp. 327-346 ◽  
Author(s):  
Thierry Cazenave
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Asymptotic Behaviour ◽  
Blow Up ◽  
Global Solutions ◽  
Two Dimensions ◽  
Linear Optics ◽  
Non Linear Optics ◽  
Non Linear ◽  
The Cauchy Problem

SynopsisThis paper is devoted to the study of some non linear Schrödinger equations in two dimensions, arising in non linear optics; in particular, it is concerned with solutions to the Cauchy problem. The problem of global existence and regularity of the solutions, the asymptotic behaviour of global solutions, and the blow-up of non global solutions are studied.

scholarly journals A nonlocal parabolic system with application to a thermoelastic problem

1999 ◽  
Vol 22 (4) ◽  
pp. 855-867
Author(s):  
Y. Lin ◽  
R. J. Tait
Keyword(s):  
Representation Theory ◽  
Parabolic System ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
System Modeling ◽  
Parabolic Systems ◽  
Thermoelastic Problem ◽  
Potential Representation

A system modeling the thermoelastic bards contacts is studied. The problem is first transformed into an equivalent nonlocal parabolic systems using a transformation, and then the existence and uniqueness of the solutions are demonstrated via the theoretical potential representation theory of the parabolic equations. Finally some realistic situations in the applications are discussed using the results obtained in this paper.

Asymptotic behaviour of solutions of the hydrodynamic model of semiconductors

2002 ◽  
Vol 132 (2) ◽  
pp. 359-378 ◽  
Author(s):  
Hailiang Li ◽  
Peter Markowich ◽  
Ming Mei
Keyword(s):  
Steady State ◽  
Asymptotic Behaviour ◽  
Small Perturbation ◽  
Hydrodynamic Model ◽  
Existence And Uniqueness ◽  
Steady State Solution ◽  
State Solution ◽  
Energy Estimates ◽  
One Dimensional ◽  
The One

Degond and Markowich discussed the existence and uniqueness of a steady-state solution in the subsonic case for the one-dimensional hydrodynamic model of semiconductors. In the present paper, we reconsider the existence and uniqueness of a globally smooth subsonic steady-state solution, and prove its stability for small perturbation. The proof method we adopt in this paper is based on elementary energy estimates.

Remarks on the asymptotic behaviour of solutions to the compressible Navier–Stokes equations in the half-line

2002 ◽  
Vol 132 (3) ◽  
pp. 627-638 ◽  
Author(s):  
Song Jiang
Keyword(s):  
Asymptotic Behaviour ◽  
Specific Volume ◽  
Stokes Equations ◽  
Global Solutions ◽  
Ideal Gas ◽  
Half Line ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Asymptotic Behaviour Of Solutions

We study the time-asymptotic behaviour of solutions to the Navier-Stokes equations for a one-dimensional viscous polytropic ideal gas in the half-line. Using a local representation for the specific volume, which is obtained by using a special cut-off function to localize the problem, and the weighted energy estimates, we prove that the specific volume is pointwise bounded from below and above for all x, t and that for all t the temperature is bounded from below and above locally in x. Moreover, global solutions are convergent as time goes to infinity. The large-time behaviour of solutions to the Cauchy problem is also examined.

Smoothing effect and asymptotic behaviour for the solutions of a nonlinear time dependent system

1981 ◽  
Vol 87 (3-4) ◽  
pp. 289-303
Author(s):  
João-Paulo Dias ◽  
Alain Haraux
Keyword(s):  
Liquid Crystals ◽  
Asymptotic Behaviour ◽  
Parabolic System ◽  
Existence And Uniqueness ◽  
Time Dependent ◽  
Generalized Solutions ◽  
Nonlinear Parabolic System ◽  
Smoothing Effect ◽  
Nonlinear Parabolic ◽  
Discontinuous Data

SynopsisIn this paper we obtain some new results on a nonlinear parabolic system related to the equations of the nematic liquid crystals and introduced in earlier papers by J. P. Dias.These results mainly concern the existence and uniqueness of generalized solutions for discontinuous data and also their asymptotic behaviour in various cases.

OPTIMAL CONTROL OF HARVESTING IN A PARABOLIC SYSTEM MODELING TWO SUBPOPULATIONS

2001 ◽  
Vol 11 (07) ◽  
pp. 1129-1141 ◽  
Author(s):  
SUZANNE M. LENHART ◽  
J. A. MONTERO
Keyword(s):  
Optimal Control ◽  
Differential System ◽  
Parabolic System ◽  
Existence And Uniqueness ◽  
System Modeling ◽  
Optimal Harvesting ◽  
Time Interval ◽  
Biological Parameters ◽  
Control Pair ◽  
Partial Differential System

An optimal harvesting problem for a parabolic partial differential system modeling two subpopulations of the same species is investigated. The two subpopulations are competing for resources. Under conditions on the smallness of the time interval and certain biological parameters, existence and uniqueness of an optimal control pair are established.

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