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.

Asymptotic behaviour of functional-differential equations with proportional time delays

1996 ◽  
Vol 7 (1) ◽  
pp. 11-30 ◽  
Author(s):  
Yunkang Liu
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Initial Value Problem ◽  
Time Delays ◽  
Functional Differential Equations ◽  
Analytic Solutions ◽  
Comprehensive Analysis ◽  
Initial Value ◽  
Functional Differential ◽  
Image Position

This paper discusses the initial value problemwhereA, BiandCiared × dcomplex matrices,pi,qi∈ (0, 1),i= 1, 2, …, andy0is a column vector in ℂd. By using ideas from the theory of ordinary differential equations and the theory of functional equations, we give a comprehensive analysis of the asymptotic behaviour of analytic solutions of this initial value problem.

scholarly journals Faedo-Galerkin approximation of mild solutions of fractional functional differential equations

2021 ◽  
Vol 8 (1) ◽  
pp. 1-17
Author(s):  
J. Vanterler da C. Sousa ◽  
Michal Fečkan ◽  
E. Capelas de Oliveira
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Galerkin Approximation ◽  
Banach Fixed Point Theorem ◽  
Convergence Results ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

Abstract In the paper, we discuss the existence and uniqueness of mild solutions of a class of fractional functional differential equations in Hilbert space separable using the Banach fixed point theorem technique. In this sense, Faedo-Galerkin approximation to the solution is studied and demonstrated some convergence results.

scholarly journals Functional Differential Equations Involving the ψ-Caputo Fractional Derivative

2020 ◽  
Vol 4 (2) ◽  
pp. 29
Author(s):  
Ricardo Almeida
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Arbitrary Function ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Derivative Operator ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

This paper is devoted to the study of existence and uniqueness of solutions for fractional functional differential equations, whose derivative operator depends on an arbitrary function. The introduction of such function allows generalization of some known results, and others can be also obtained.

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

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

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