A new method to obtain decay rate estimates for dissipative systems with localized damping (Q1300574)

Using a piece-wise multiplier method and new integral inequalities the author gives a precise asymptotic estimate of the solutions to the initial boundary value problem for the equation \(u_{tt}-\triangle u +f(x,u_t)=0\) \((x\in \Omega \subset \mathbb{R}^n\), \(t>0)\) with Dirichlet boundary conditions. As an application of the theory there is discussed the energy decay for elastodynamic system with locally distributed damping.