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We examine the wave equation in the exterior of a strictly convex boundeddomain $K$ with dissipative boundary condition $\partial_{\nu} u - \gamma(x)\partial_t u = 0$ on the boundary $\Gamma$ and $0 < \gamma(x) <1, \:\forall x\in \Gamma.$ The solutions are described by a contraction semigroup $V(t) =e^{tG}, \: t \geq 0.$ The poles of the meromorphic incoming resolvent $(G -\lambda)^{-1}: \: {\mathcal H}_{comp} \rightarrow {\mathcal D}_{loc}$ areeigenvalues of G if ${\rm Re}\: \lambda < 0$ and incoming resonances if ${\rmRe}\: \lambda > 0$. We obtain sharper results for the location of theeigenvalues of $G$ and incoming resonances in $\Lambda = \{\lambda \in {\mathbbC}:\: |{\rm Re}\: \lambda| \leq C_2(1 + |{\rm Im}\: \lambda|)^{-2},\: |{\rmIm}\: \lambda| \geq A_2 > 1\}$ and we prove a Weyl formula for theirasymptotic. For $K = \{x \in {\mathbb R}^3:\:|x| \leq 1\}$ and $\gamma$constant we show that $G$ has no eigenvalues so the Weyl formula concerns onlythe incoming resonances.

Eigenvalues and resonances of dissipative acoustic operator for strictly convex obstacles