LOCAL DECAY FOR THE DAMPED WAVE EQUATION IN THE ENERGY SPACE

Local decay for the damped wave equation in the energy space

Achieving Arbitrarily Large Decay in the Damped Wave Equation

is referred to as the decay rate associated with a. If a is to be introduced in order to absorb an initial disturbance then one naturally wishes to strike upon that a with the least possible (most negative) decay rate. The mathematical attraction here lies in the oftnoted fact that, with respect to damping, ‘more is not better.’ More precisely, for constant a, the decay rate is not a decreasing...

Energy decay for the damped wave equation under a pressure condition

We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with respect to the geodesic flow. As an application, we show an exponential decay of the energy for all initial data sufficiently regular. This decay is governed by...

Weighted energy decay for 3D wave equation

We obtain a dispersive long-time decay in weighted energy norms for solutions to the 1D wave equation with generic potential. The decay extends the results obtained by Murata for the 1D Schrödinger equation.

Energy decay for damped wave equations on partially rectangular domains

We consider the wave equation with a damping term on a partially rectangular planar domain, assuming that the damping is concentrated close to the non-rectangular part of the domain. Polynomial decay estimates for the energy of the solution are established.