Exponential decay for the damped wave equation in unbounded domains

Romain Joly (1)

1 IF - Institut Fourier

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.

Mots clés: damped wave equation; exponential decay; uniform stabilisation; variable damping; unbounded domains

Domaines: Equations aux dérivées partielles [math.AP]

Romain Joly. Exponential decay for the damped wave equation in unbounded domains. 2014. ⟨hal-01058120v1⟩