Exponential decay of solutions of a nonlinearly damped wave equation
نویسنده
چکیده
The issue of stablity of solutions to nonlinear wave equations has been addressed by many authors. So many results concerning energy decay have been established. Here in this paper we consider the following nonlinearly damped wave equation utt −∆u+ a(1 + |ut|)ut = bu|u|p−2, a, b > 0, in a bounded domain and show that, for suitably chosen initial data, the energy of the solution decays exponentially even if m > 2. 2000 Mathematics Subject Classification: 35L45.
منابع مشابه
Exponential Decay Rates for the Damped Korteweg-de Vries Type Equation
The exponential decay rate of L−norm related to the Korteweg-de Vries equation with localized damping posed on the whole real line is established. In addition, using classical arguments we determine that the solutions associated to the fully damped Korteweg-de Vries equation do not decay in H− level for arbitrary initial data.
متن کاملDecay of solutions of a degenerate hyperbolic equation ∗
This article studies the asymptotic behavior of solutions to the damped, non-linear wave equation ü+ γu̇−m(‖∇u‖)∆u = f(x, t) , which is known as degenerate if the greatest lower bound for m is zero, and non-degenerate if the greatest lower bound is positive. For the nondegenerate case, it is already known that solutions decay exponentially, but for the degenerate case exponential decay has remai...
متن کاملDecay estimates of solutions to the IBq equation
In this paper we focus on the Cauchy problem for the generalized IBq equation with damped term in $n$-dimensional space. We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value, provided that the initial value is suitably small. Moreover, we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...
متن کاملEnergy decay for the damped wave equation under a pressure condition
We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with respect to the geodesic flow. As an application, we show an exponential decay of the energy for all initial data sufficiently regular. This decay is governed by...
متن کاملDecay of Solutions of the Wave Equation with Localized Nonlinear Damping and Trapped Rays
We prove some decay estimates of the energy of the wave equation governed by localized nonlinear dissipations in a bounded domain in which trapped rays may occur. The approach is based on a comparison with the linear damped wave equation and an interpolation argument. Our result extends to the nonlinear damped wave equation the well-known optimal logarithmic decay rate for the linear damped wav...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005