A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. The main aim of the note is to show that under the standard dissipativity restrictions on the nonlinearities involved the initial boundary value problem for the considered equation is globally well-posed in the class of sufficiently regular solutions and ...

We study the Cauchy problem for a nonlinear damped wave equation. Under suitable assumptions for the nonlinearity and the initial data, we obtain the global solution which satisfies weighted L and L∞ estimates. Furthermore, we establish the higher order asymptotic expansion of the solution. This means that we construct the nonlinear approximation of the global solution with respect to the weigh...

We consider a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacement which is coupled to an elliptic equation for the electrostatic potential. We first review some recent results on existence and nonexistence of steady-states as well as on local and global well-posedness of the dyn...

In this paper we consider a nonlinear strongly damped wave equation as a model for a controlled spring–mass–damper system and give some results concerning its large time behaviour. It can be seen that the infinite dimensional system admits a twodimensional attracting manifold where the equation is well represented by a classical nonlinear oscillations ODE, which can be exhibited explicitly. In ...

We study the effects of large diffusivity in all parts of the domain in a linearly damped wave equation subject to standard zero Robin-type boundary conditions. In the linear case, we show in a given sense that the asymptotic behaviour of solutions verifies a second-order ordinary differential equation. In the semilinear case, under suitable dissipative assumptions on the nonlinear term, we pro...

We present the stochastic Schrödinger equation for the dynamics of a quantum particle coupled to a high temperature environment and apply it to the dynamics of a driven, damped, nonlinear quantum oscillator. Apart from an initial slip on the environmental memory time scale, in the mean, our result recovers the solution of the known non-Lindblad quantum Brownian motion master equation. A remarka...

A kinetic theory of linear electrostatic plasma waves with frequencies near the cyclotron frequency Ωcs of a given plasma species s is developed for a multispecies nonneutral plasma column with general radial density and electric field profiles. Terms in the perturbed distribution function up to O(1/Ωcs) are kept, as are the effects of finite cyclotron radius rc up to O(r 2 c ). At this order t...

in this paper, we present a comparative study between the adomian decomposition method and two classical well-known runge-kutta and central difference methods for the solution of damped forced oscillator problem. we show that the adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply.