GENERAL DECAY OF SOLUTIONS OF NONLINEAR VISCOELASTIC WAVE EQUATION
نویسندگان
چکیده
منابع مشابه
General Decay of Solutions for a Viscoelastic Equation with Balakrishnan-taylor Damping
Abstract. A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions on the relaxation function and with certain initial data and by adopting the perturbed energy method, we establish uniform decay rate of the solution energy in terms of the behavior of the relaxation function, which are not n...
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 کاملUniform Decay Rates of Solutions to a Nonlinear Wave Equation with Boundary Condition of Memory Type
In this article we study the hyperbolic problem (1) where R is a bounded region in Rn whose boundary is partitioned into disjoint sets ro, rl. We prove that the dissipation given by the memory term is strong enough to assure exponential (or polynomial) decay provided the relaxation function also decays exponentially (or polynomially). In both cases the solution decays with the same rate of the ...
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 کاملExponential decay of solutions of a nonlinearly damped wave equation
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 exponenti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: East Asian mathematical journal
سال: 2016
ISSN: 1226-6973
DOI: 10.7858/eamj.2016.045