Uniform Decay Rates of Solutions to a Structural Acoustics Model with Nonlinear Dissipation
نویسنده
چکیده
In this work, the asymptotic behavior of solutions to a coupled hyperbolic/parabolic{like system is investigated. It is shown that with both components of the equation being subjected to nonlinear damping (boundary damping for the wave component, interior for the beam), a global uniform stability is attained for all (weak) solutions.
منابع مشابه
Dissipative Property of the Vlasov-Maxwell-Boltzmann System with a Uniform Ionic Background
In this paper we discuss the dissipative property of near-equilibrium classical solutions to the Cauchy problem of the Vlasov-Maxwell-Boltzmann System in the whole space R3 when the positive charged ion flow provides a spatially uniform background. The most key point of studying this coupled degenerately dissipative system here is to establish the dissipation of the electromagnetic field which ...
متن کاملAsymptotics in Nonlinear Evolution System with Dissipation and Ellipticity on Quadrant
In this paper, we consider an initial boundary value problem for some nonlinear evolution system with dissipation and ellipticity. We establish the global existence and furthermore obtain the Lp (p ≥ 2) decay rates of solutions corresponding to diffusion waves. The analysis is based on the energy method and pointwise estimates.
متن کاملGlobal Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation
The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku'' + M(|A (1/2) u|(2))Au + g(u') = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations ...
متن کاملGlobal Existence and Decay of Energy to Systems of Wave Equations with Damping and Supercritical Sources
This paper is concerned with a system of nonlinear wave equations with supercritical interior and boundary sources, and subject to interior and boundary damping terms. It is well-known that the presence of a nonlinear boundary source causes significant difficulties since the linear Neumann problem for the single wave equation is not, in general, well-posed in the finite-energy space H(Ω) × L(∂Ω...
متن کاملA fractional Burgers equation arising in nonlinear acoustics: theory and numerics
The study of a fractional Burgers equation arising in nonlinear acoustics is presented. The motivation comes from an elementary model of shock waves in brass wind instruments, that proves useful in musical acoustics. Such a model results from the coupling of a conservative nonlinear system with a dissipative term; here the dissipation is represented by a fractional derivative in time, for which...
متن کامل