A new method to obtain decay rate estimates for dissipative systems with localized damping
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.
elastodynamic system with locally distributed damping
scientific article; zbMATH DE number 1330686