Weyl formula for the eigenvalues of the dissipative acoustic operator
Vesselin M. Petkov · arXiv (Cornell University) · 2021
We study the wave equation in the exterior of a bounded domain $K$ with dissipative boundary condition $\partial_ν u - γ(x) \partial_t u = 0$ on the boundary $Γ$ and $γ(x) > 0.$ The solutions are described by a contraction semigroup $V(t) = e^{tG}, \: t \geq 0.$ The eigenvalues $λ_k$ of $G$ with ${\rm Re}\: λ_k 1.$ For strictly convex obstacles $K$ this formula concerns all eigenvalues of $G.$