This paper describes the physical relationships that exist between the Fourier transform and the response spectrum of a strong-motion accelerogram. By developing the new concept of the "Damped Fourier Spectrum" (D.F.S.), we show that the velocity and displacement of the damped oscillator can be represented by a linear combination of the real and imaginary parts of the D.F.S. and by the initial ...

We study the asymptotic behavior of solutions to the stochastic strongly damped wave equation with additive noise defined on unbounded domains. We first prove the uniform estimates of solutions, and then establish the existence of a random attractor.

In the aim to find simplest and most efficient shape of a noise absorbing wall dissipate acoustical energy sound wave, we consider frequency model described by Helmholtz equation with damping on boundary. The well-posedness is shown in class domains $d$-set boundaries ($N-1\le d<N$). We introduce admissible Lipschitz boundaries, which an optimal exists following sense: prove existence Radon mea...

This talk describes some applications of two kinds of observation estimate for the wave equation and for the damped wave equation in a bounded domain where the geometric control condition of C. Bardos, G. Lebeau and J. Rauch may failed. 1 The wave equation and observation We consider the wave equation in the solution u = u(x, t)    ∂ t u−∆u = 0 in Ω× R , u = 0 on ∂Ω× R , (u, ∂tu) (·, 0) = (u...

We study the damped wave equation with time-dependent coefficients utt(t, x) − a(t) 2 ∆u(t, x) − b ′ b (t)ut(t, x) = 0 in R n and prove energy estimates for a new class of coefficients.

In this paper the interaction of attosecond laser pulses with matter is investigated. The scattering and potential motion of heat carriers as well as the external force are considered. Depending on the ratio of the scatterings and potential motion the heat transport is described by the thermal forced Klein-Gordon or thermal modified telegraph equation. For thermal Heisenberg type relation V τ ∼...

In this paper the Variational Iteration Method (VIM) is used to investigate the damped generalized regularized long-wave equation(DGRLW). The solution of the nonlinear DGRLW equation is calculated in the form of series with computable components. Numerical examples are tested to illustrate the proposed scheme. Moreover, the approximate solutions are compared with the exact solutions.