Degenerate Damping Research Articles

Stability for degenerate wave equations with drift under simultaneous degenerate damping

In this paper we study the stability of two different problems. The first one is a one-dimensional degenerate wave equation with degenerate damping, incorporating a drift term and a leading operator in non-divergence form. In the second problem we consider a system that couples degenerate and non-degenerate wave equations, connected through transmission, and subject to a single dissipation law at the boundary of the non-degenerate equation. In both scenarios, we derive exponential stability results.

Stationary measures for stochastic differential equations with degenerate damping

Stationary measures for stochastic differential equations with degenerate damping

General decay and blow-up of solution for a viscoelastic wave equation with nonlinear degenerate damping and source terms

We are concerned with the initial-boundary value problem for a nonlinear viscoelastic problem with the degenerate damping and the nonlinear source term in this paper. Under appropriate assumptions on the initial data, memory kernel and parameters, we establish several results regarding the global solution, blow-up properties and general decay in the case of positive initial energy. We overcome the difficulties brought by positive initial energy by using the potential well theory.

Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term

In this paper, we consider a Kirchhoff-type viscoelastic equation with degenerate damping term have initial and Dirichlet boundary conditions. We obtain the blow up and exponential growth of solutions with negative initial energy.

Global nonexistence of solution for coupled nonlinear Klein-Gordon with degenerate damping and source terms

"In this article we consider a coupled system of nonlinear Klein-Gordon equations with degenerate damping and source terms. We prove, with positive initial energy, the global nonexistence of solutions by concavity method."

Stability of Solutions for a Krichhoff-Type Plate Equation with Degenerate Damping

We investigate a Kirchhoff type plate equation with degenerate damping term. By potential well theory, we show the asymptotic stability of energy in the presence of a degenerate damping.

Stability result for a variable-exponent viscoelastic double-Kirchhoff type inverse source problem with nonlocal degenerate damping term

Stability result for a variable-exponent viscoelastic double-Kirchhoff type inverse source problem with nonlocal degenerate damping term

Global Existence And Growth Of Solutions To Coupled Degeneratly Damped Klein-Gordon Equations

We study a system of nonlinear Klein-Gordon equations with viscoelastic and degenerate damping in a bounded domain. We prove the global existence and exponential growth of solutions with negative initial energy.

Exponential growth of positive initial energy solutions for coupled nonlinear Klein-Gordon equations with degenerate damping and source terms

In this paper we will prove that the positive initial-energy solution for coupled nonlinear Klein-Gordon equations with degenerate damping and source terms grows exponentially.

"Global nonexistence of solutions to system of Klein-Gordon equations with degenerate damping and strong source terms in viscoelasticity"

In this paper, we consider a system of nonlinear viscoelastic wave equations with degenerate damping and source terms. We prove, with positive initial energy, the global nonexistence of solution by concavity method.

Existence, blow up and growth of solutions for a coupled quasi-linear viscoelastic Petrovsky equations with degenerate damping terms

We consider a quasi-linear coupled system of two viscoelastic equations with degenerate damping and source terms under the Dirichlet boundary condition. We obtain the global existence, blow up and exponential growth of solutions under some restrictions on the initial data, relaxation functions and degenerate damping terms.

Blow-Up of Solutions for a Coupled Nonlinear Viscoelastic Equation with Degenerate Damping Terms: Without Kirchhoff Term

In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping and source terms without the Kirchhoff term. Under suitable hypothesis, we study the blow-up of solutions.

Blow-up of solutions for a quasilinear system with degenerate damping terms

In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping and general source terms. According to some suitable hypothesis, we study the blow-up of solutions. This is the general case of the recent results of Boulaaras’ works (Bull. Malays. Math. Sci. Soc. 43:725–755, 2020) and (Appl. Anal. 99:1724–1748, 2020).

Blow Up and Exponential Growth to a Petrovsky Equation with Degenerate Damping

This paper deals with the initial boundary value problem of Petrovsky type equation with degenerate damping. Under some appropriate conditions, we study the finite time blow up and exponential growth of solutions with negative initial energy.

Global Existence and General Decay of Solutions for a Quasilinear System with Degenerate Damping Terms

In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping, dispersion, and source terms under Dirichlet boundary condition. Under some restrictions on the initial datum and standard conditions on relaxation functions, we study global existence and general decay of solutions. The results obtained here are generalization of the previous recent work.

Stability for extensible beams with a single degenerate nonlocal damping of Balakrishnan-Taylor type

In this paper, motivated by recent papers on the stabilization of evolution problems with nonlocal degenerate damping terms, we address an extensible beam model with degenerate nonlocal damping of Balakrishnan-Taylor type. We discuss initially on the well-posedness with respect to weak and regular solutions. Then we show for the first time how hard is to guarantee the stability of the energy solution (related to regular solutions) in the scenarios of constant and non-constant coefficient of extensibility. The degeneracy (in time) of the single nonlocal damping coefficient and the methodology employed in the stability approach are the main novelty for this kind of beam models with degenerate damping.

Growth of solutions with $ L^{2(p+2)} $-norm for a coupled nonlinear viscoelastic Kirchhoff equation with degenerate damping terms

<abstract><p>In this work, we consider a coupled nonlinear viscoelastic Kirchhoff equations with degenerate damping, dispersion and source terms. Under suitable hypothesis, we will prove that when the initial data are large enough (in the energy point of view), the energy grows exponentially and thus so the $ L^{2(p+2)} $-norm.</p></abstract>

Growth of solutions for fourth order viscoelastic system

We consider a system of viscoelastic equations with degenerate damping and source terms under Dirichlet boundary condition. We prove the exponential growth of solutions under some restrictions on the initial data, relaxation functions and degenerate damping terms.

Local existence and blow up of solutions for a coupled viscoelastic Kirchhoff-type equation with degenerate damping

Local existence and blow up of solutions for a coupled viscoelastic Kirchhoff-type equation with degenerate damping

Asymptotic stability and blow-up for the wave equation with degenerate nonlocal nonlinear damping and source terms

This work is devoted to studying a wave equation with degenerate nonlocal nonlinear damping and source terms. By potential well theory, we show the asymptotic stability of energy in the presence of a degenerate damping of polynomial type when the initial energy is small. Also, we firstly derive some sufficient conditions on initial data which lead to finite time blow-up.