Balakrishnan-Taylor Damping Research Articles

Blow-up of solutions for a viscoelastic Kirchhoff equation with a source, delay and Balakrishnan-Taylor damping terms

A nonlinear viscoelastic Kirchhoff-type equation with a source, Balakrishnan-Taylor damping, dispersion and delay terms is studied. We prove the blow-up of solutions under suitable hypotheses.

Blow-up of Solutions for a Problem with Balakrishnan-Taylor Damping and Nonlocal Singular Viscoelastic Equations

In this paper, we study the nonlinear one-dimensional viscoelastic nonlocal problem 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.

Asymptotic behavior for a class of logarithmic wave equations with Balakrishnan-Taylor damping, nonlinear weak damping and strong linear damping

<abstract><p>In spaces with any dimension, a class of logarithmic wave equations with Balakrishnan-Taylor damping, nonlinear weak damping and strong linear damping was considered</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ {u_{tt}} - M(t)\Delta u + \left( {g * \Delta u} \right)(t) + h({u_t}){u_t} - \Delta {u_t} + f(u) + u = u\ln {\left| u \right|^k} $\end{document} </tex-math></disp-formula></p> <p>with Dirichlet boundary condition. Under a set of specified assumptions, we established the existence of global weak solutions and elucidated the decay rate of the energy function for particular initial data. This contribution extended and surpassed prior investigations, as documented by A. Peyravi (2020), which omitted the consideration of Balakrishnan-Taylor damping and strong linear damping while being confined to three spatial dimensions. Our findings underscored the pivotal role of these overlooked damping factors. Furthermore, our demonstration underscored that Balakrishnan-Taylor damping, weak damping and strong damping collectively induced an exponential decay, although the precise nature of this decay was contingent upon the differentiable function associated with the memory damping term $ {\zeta (t)} $. Consequently, the absence of the damping term in reference by A. Peyravi (2020) was unequivocally shown not to augment the decay rate. This insight enhanced our understanding of the nuanced dynamics involved and contributed to the refinement of existing models.</p></abstract>

On the exponential decay of a Balakrishnan-Taylor plate with strong damping

<abstract><p>In this manuscript, we study a thin and narrow plate equation that models the deck of a suspension bridge that is subject to a Balakrishnan-Taylor damping and a strong damping. First, by using the Faedo Galerkin method, we prove the existence of both global weak and regular solutions. Second, we prove the exponential stability of the energy for regular solutions by combining the multiplier method and a well-known result of Komornik.</p></abstract>

Initial boundary value problem for a viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term: decay estimates and blow-up result

In this paper, we study the initial boundary value problem for the following viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term where the relaxation function satisfies g'(t)leq -xi (t)g^{r}(t), tgeq 0, 1leq r< frac{3}{2}. The main goal of this work is to study the global existence, general decay, and blow-up result. The global existence has been obtained by potential-well theory, the decay of solutions of energy has been established by introducing suitable energy and Lyapunov functionals, and a blow-up result has been obtained with negative initial energy.

Uniform stability of a strong time-delayed viscoelastic system with Balakrishnan–Taylor damping

This paper studies a Balakrishnan–Taylor viscoelastic wave equation with strong time-dependent delay. Under suitable assumptions on the coefficients of the delay term, we establish a generalized stability result, which improve some earlier results in the literature.

Asymptotic expansion of solutions for the Robin-Dirichlet problem of Kirchhoff-Carrier type with Balakrishnan-Taylor damping

In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with Balakrishnan-Taylor damping. First, under suitable conditions on the initial data, the local existence and uniqueness of a weak solution are proved. Next, an asymptotic expansion of solutions in a small parameter with high order is established. The used main tools are the linearization method for nonlinear terms together with the Faedo-Galerkin method, and the key lemmas of the expansion of high-order polynomials and the Taylor expansion for multi-variable functions.

General decay estimate for a viscoelastic wave equation with Balakrishnan-Taylor damping and strong dissipation

General decay estimate for a viscoelastic wave equation with Balakrishnan-Taylor damping and strong dissipation

Global existence and asymptotic behavior for a viscoelastic Kirchhoff equation with a logarithmic nonlinearity, distributed delay and Balakrishnan-Taylor damping terms

&lt;abstract&gt;&lt;p&gt;A nonlinear viscoelastic Kirchhoff-type equation with a logarithmic nonlinearity, Balakrishnan-Taylor damping, dispersion and distributed delay terms is studied. We establish the global existence of the solutions of the problem and by the energy method we prove an explicit and general decay rate result under suitable hypothesis.&lt;/p&gt;&lt;/abstract&gt;

General decay rate for a viscoelastic wave equation with distributed delay and Balakrishnan-Taylor damping

Abstract A nonlinear viscoelastic wave equation with Balakrishnan-Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

On the viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources with variable-exponent nonlinearities

This work is devoted to the study of a nonlinear viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping and nonlinear boundary interior sources with variable exponents. Under appropriate assumptions, we establish a uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.

General decay result of solutions for viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term

In this paper, we consider a viscoelastic wave equation with Balakrishnan–Taylor damping and a delay term. Under suitable assumptions on relaxation functions, we establish general decay result for energy.

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.

Decay of energy for viscoelastic wave equations with Balakrishnan-Taylor damping and memories

In this article, we consider a viscoelastic wave equation with Balakrishnan-Taylor damping, and finite and infinite memory terms in a bounded domain. Under suitable assumptions on relaxation functions and with certain initial data, by adopting the perturbed energy method, we establish a decay of energy which depends on the behavior of the relaxation functions.&#x0D; For more information see https://ejde.math.txstate.edu/Volumes/2020/42/abstr.html

Decay rates for a viscoelastic wave equation with Balakrishnan-Taylor and frictional dampings

In this paper we are concerned with a viscoelastic wave equation with Balakrishnan-Taylor damping and frictional damping. By using the multiplier method and some properties of convex functions, we establish general energy decay rates of the equation without imposing any growth assumption near the origin on the frictional term and strongly weakening the usual assumptions on the relaxation term. Our stability result generalizes the earlier related results.

General decay rate for weak viscoelastic wave equation with Balakrishnan–Taylor damping and time-varying delay

A weak viscoelastic wave equation with Balakrishnan–Taylor damping and internal time-varying delay in a bounded domain is considered. The Balakrishnan–Taylor damping appears in the flutter panel equation and the spillover problem which was initially proposed by Balakrishnan and Taylor in 1989. The presence of delay may be a source of instability. Under appropriate assumptions on the source term, with the relaxation function and certain initial data and by adopting the perturbed energy method, we establish general decay estimate for the energy, which depends on the behavior of the relation function, and which is not necessarily decaying in a polynomial or exponential fashion..

Stabilization for wave equation of variable coefficients with Balakrishnan–Taylor damping and source term

In this paper, we consider the wave equation of variable coefficients with Balakrishnan–Taylor damping, time-varying delay and source term. By establishing some Lyapunov functionals which are equivalent to the energy of the system and using the potential well method to deal with the source term, we prove a general stability result.

On the viscoelastic equation with Balakrishnan-Taylor damping and acoustic boundary conditions

In this paper, we consider the viscoelastic equation with Balakrishnan-Taylor damping and acoustic boundary conditions. This work is devoted to prove, under suitable conditions on the initial data, the global existence and uniform decay rate of the solutions when the relaxation function is not necessarily of exponential or polynomial type.

Asymptotic Stability of the Viscoelastic Equation with Variable Coefficients and the Balakrishnan-Taylor Damping

In this paper, we consider the viscoelastic equation with variable coefficients and Balakrishnan-Taylor damping and source terms. This work is devoted to prove, under suitable conditions on the initial data, the asymptotic stability without imposing any restrictive growth assumption on the damping term and weakening of the usual assumptions on the relaxation function.

Stabilization for the Wave Equation with Variable Coefficients and Balakrishnan-Taylor Damping

In this paper, we consider the wave equation with variable coefficients and Balakrishnan-Taylor damping and source terms. This work is devoted to prove, under suitable conditions on the initial data, the uniform decay rates of the energy without imposing any restrictive growth near zero assumption on the damping term.