Weyl formula for the eigenvalues of the dissipative acoustic operator

We study the wave equation in exterior of a bounded domain K with dissipative boundary condition $$\partial _{\nu } u - \gamma (x) \partial _t = 0$$ on $$\Gamma $$ and $$\gamma > 0.$$ The solutions are described by contraction semi-group $$V(t) e^{tG}, \, t \ge eigenvalues $$\lambda _k$$ G $$\text{ Re }\,\lambda _k < yield asymptotically disappearing $$u(t, x) e^{\lambda t} f(x)$$ having exponentially decreasing global energy. establish Weyl formula for these case $$\min _{x\in \Gamma 1.$$ For strictly convex obstacles K, this concerns all G.