Exponential decay for the damped wave equation in unbounded domains
Résumé
We discuss the exponential decay of the semigroup generated by the damped wave equation in an unbounded domain. A typical result is the following. Let $\gamma \in L^\infty(R^d)$ be a periodic non-negative damping such that there exists a length L > 0 such that any segment of $R^d$ of length L intersects the set $\{ x \in R^d, \gamma (x) > 0\}$. Then, the linear semigroup associated to the damped wave equation $u_{tt}+\gamma(x)u_t=\Delta u - u$ is decaying exponentially fast.
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