Energy decay of solutions of dissipative wave equations
نویسندگان
چکیده
منابع مشابه
Decay Rates for Dissipative Wave equations
We derive decay rates for the energy of solutions of dissipative wave equations. The metod of proof combines multiplier techniques and the construction of suitable Lyapunov functionals. Without imposing any growth condition at the origin on the nonlinearity we show that this Lyapunov functional, which is equivalent to the energy of the system, is bounded above by the solution of a differential ...
متن کاملPeriodic Wave Shock solutions of Burgers equations
In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...
متن کاملThe Energy Decay Problem for Wave Equations with Nonlinear Dissipative Terms in R
We study the asymptotic behavior of energy for wave equations with nonlinear damping g(ut) = |ut|m−1ut in Rn (n ≥ 3) as time t → ∞. The main result shows a polynomial decay rate of energy under the condition 1 < m ≤ (n+2)/(n+1). Previously, only logarithmic decay rates were found.
متن کاملResponse Solutions for Quasi-Periodically Forced, Dissipative Wave Equations
We consider several models of nonlinear wave equations subject to very strong damping and quasi-periodic external forcing. This is a singular perturbation, since the damping is not the highest order term. We study the existence of response solutions (i.e., quasi-periodic solutions with the same frequency as the forcing). Under very general non-resonance conditions on the frequency, we show the ...
متن کاملDecay estimates of solutions to wave equations in conical sets
We consider the wave equation in an unbounded conical domain, with initial conditions and boundary conditions of Dirichlet or Neumann type. We give a uniform decay estimate of the solution in terms of weighted Sobolev norms of the initial data. The decay rate is the same as in the full space case.
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: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1977
ISSN: 0386-2194
DOI: 10.3792/pjaa.53.232