Global existence and nonexistence for some degenerate and quasilinear parabolic systems

The author discusses the degenerate and quasilinear parabolic system

     

Global attractor for a class of nonlinear lattices

We consider a class of nonlinear lattices with nonlinear damping

(0.1)     

Boundedness in a chemotaxis model with oxygen consumption by bacteria

This paper deals with the Keller-Segel model

     

Global existence results for impulsive differential equations

This paper studies the global existence of solutions of the impulsive differential equation

     

Global stability for nonlinear difference equations with variable coefficients

Consider the following nonlinear difference equation with variable coefficients:

     

Chemotaxis with logistic source: Very weak global solutions and their boundedness properties

We consider the chemotaxis system

     

On global periodicity of difference equations

In this research, we consider a difference equation of order k?2 of the following form:

     

Existence and nonexistence of a global solution for coupled nonlinear wave equations with damping and source

We consider the system of nonlinear wave equations

     

Global asymptotic stability of a family of difference equations

We consider the family of difference equations of the form

     

Global behavior of a discrete haematopoiesis model with several delays

In this paper, we study the difference equation:

     

Global attractivity for half-linear differential systems with periodic coefficients

The system to be considered in this paper is

     

On the global attractivity for a logistic equation with piecewise constant arguments

In this paper, we consider the following logistic equation with piecewise constant arguments:

     

A global stability criterion in nonautonomous delay differential equations

Consider the following nonautonomous nonlinear delay differential equation:

     

Exponential energy decay of solutions of viscoelastic wave equations

In this paper we consider the nonlinear viscoelastic equation

     

Global attractor for the Ginzburg-Landau thermoviscoelastic systems with hinged boundary conditions

This paper is concerned with the following one-dimensional nonlinear system of equations:

(0.1)     

Quenching Phenomenon for a Parabolic MEMS Equation

This paper deals with the electrostatic MEMS-device parabolic equation u_t-?u =λf(x)/(1-u)~p in a bounded domain ? of R~N,with Dirichlet boundary condition,an initial condition u0(x) ∈ [0,1) and a nonnegative profile f,where λ 0,p 1.The study is motivated by a simplified micro-electromechanical system(MEMS for short) device model.In this paper,the author first gives an asymptotic behavior of the quenching time T*for the solution u to the parabolic problem with zero initial data.Secondly,the author investigates when the solution u will quench,with general λ,u0(x).Finally,a global existence in the MEMS modeling is shown.     

Local and global well-posedness for the 2D generalized Zakharov-Kuznetsov equation

This paper addresses well-posedness issues for the initial value problem (IVP) associated with the generalized Zakharov-Kuznetsov equation, namely,

     

Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source

In this paper we investigate the global existence and finite time blow-up of solutions to the system of nonlinear viscoelastic wave equations

in Ω×(0,T) with initial and Dirichlet boundary conditions, where Ω is a bounded domain in . Under suitable assumptions on the functions g_i(), , the initial data and the parameters in the equations, we establish several results concerning local existence, global existence, uniqueness and finite time blow-up property.     

Global asymptotic stability of a higher order rational difference equation

In this note, we consider the following rational difference equation:

     

Global asymptotic stability and oscillation of a family of difference equations

We consider the family of difference equations of the form