System Of Nonlinear Viscoelastic Equations Research Articles

Blow-Up of Solutions for a System Viscoelastic Equation with Balakrishnan–Taylor Damping and Nonlinear Source of Polynomial Type

In this paper, we study the initial-boundary value problem for a system of nonlinear viscoelastic equations with Balakrishnan–Taylor damping terms and nonlinear source of polynomial type. We demonstrate that the nonlinear source of polynomial type is able to force solutions to blow up infinite time even in presence of stronger damping with non positive initial energy combined with a positive initial energy.

General decay for a coupled Lamé system of nonlinear viscoelastic equations

In this paper, we consider a coupled Lamé system of nonlinear viscoelastic equations with general source terms. Under some suitable conditions on the initial data and the relaxation functions, we prove an asymptotic stability result of global solution taking into account that the kernel is not necessarily decreasing. This work generalizes and improves earlier results in the literature.

Decay rates for a coupled quasilinear system of nonlinear viscoelastic equations

Abstract In this paper, we consider a nonlinear quasilinear system of two coupled viscoelastic equations and investigate the asymptotic behavior of this system. We establish an explicit and general formula for the energy decay rates. Our result allows a wider class of relaxation functions, which improves earlier results existing in the literature.

Well posedness and asymptotic behavior of a coupled system of nonlinear viscoelastic equations

In this paper, we consider a nonlinear system of two coupled viscoelastic equations which describes the interaction between two different fields arising in viscoelasticity. We prove the well-posedness and, for a wider class of relaxation functions, establish a generalized stability result for this system.

Blow Up of Solutions for a Viscoelastic System with Damping and Source Terms in IRn

This paper deals with a Cauchy problem for the coupled system of nonlinear viscoelastic equations with damping and source terms. We prove a new finite time blow-up result for compactly supported initial data with non-positive initial energy as well as positive initial energy by using the modified energy method and the compact support technique.

Polynomial stability of solutions for a system of non-linear viscoelastic equations

In this article, we consider an interacting system consisting of two weakly-coupled viscoelastic equations. This work proves a uniform stabilization result without assuming any decay rate of the relaxation function provided that the kernels have some flat zones, the size of the flat zones are sufficiently small.

Blow Up of Solutions for a System of Nonlinear Viscoelastic Equations with Damping Terms in Rn

Abstract We consider a coupled system of nonlinear viscoelastic equations with linear damping and source terms. Under suitable conditions of the initial data and the relaxation functions, we prove a finitetime blow-up result with vanishing initial energy by using the modified energy method and a crucial lemma on differential inequality