Stochastic wave equations with dissipative damping

Wave equations with non-dissipative damping

On Damping Rates of dissipative KdV equations

We consider here different models of dissipative Korteweg-de Vries (KdV) equations on the torus. Using a proper wave function Γ, we compare numerically the long time behavior effects of the damping models and we propose a hierarchy between these models. We also introduce a method based on the solution of an inverse problem to rebuild a posteriori the damping operator using only samples of the s...

A Linear Difference Scheme for Dissipative Symmetric Regularized Long Wave Equations with Damping Term

We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term by finite difference method. A linear three-level implicit finite difference scheme is designed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is of second-order convergence and unconditionally stable by the discrete energ...

Nonlinear Dissipative Wave Equations with Potential

We study the long time behavior of solutions of the wave equation with absorbtion |u|p−1u and variable damping V (x)ut, where V (x) ∼ V0|x|−α for large |x|, V0 > 0. For α ∈ [0, 1) and 1 < p < (n + 2)/(n − 2) we establish decay estimates of the energy, L2 and Lp+1 norm of solutions. We find three different regimes of decay of solutions depending on the exponent of the absorbtion term. We show th...

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 ...