The damped wave equation in a moving domain

Damped Wave Equation with a Critical Nonlinearity

We study large time asymptotics of small solutions to the Cauchy problem for nonlinear damped wave equations with a critical nonlinearity { ∂2 t u+ ∂tu−∆u+ λu 2 n = 0, x ∈ Rn, t > 0, u(0, x) = εu0 (x) , ∂tu(0, x) = εu1 (x) , x ∈ Rn, where ε > 0, and space dimensions n = 1, 2, 3. Assume that the initial data u0 ∈ H ∩H, u1 ∈ Hδ−1,0 ∩H−1,δ, where δ > n 2 , weighted Sobolev spaces are H = { φ ∈ L; ...

[hal-00829857, v1] Null controllability of the structurally damped wave equation with moving point control

We investigate the internal controllability of the wave equation with structural damping on the one dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove that the null controllability holds in some suitable Sobolev space and after a fixed positive time independent of the initial conditions.

Mixed Spectral and Pseudospectral Methods for a Nonlinear Strongly Damped Wave Equation in an Exterior Domain

The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc, using Fourier and generalized Laguerre functions. As an example, we consider a nonlinear strongly damped wave equation. The mixed spectral and pseudospectral schemes are proposed. The convergence is proved. Numerical results demonstrate the efficiency of this approach. AMS su...

Blow Up in a Nonlinearly Damped Wave Equation

In this paper we consider the nonlinearly damped semilinear wave equation utt −∆u + aut |ut|m−2 = bu|u|p−2 associated with initial and Dirichlet boundary conditions. We prove that any strong solution, with negative initial energy, blows up in finite time if p > m. This result improves an earlier one in [2].

Global Nonexistence in a Nonlinearly Damped Wave Equation