Abstract:We study the wave equation in the exterior of a strictly convex bounded domain $K \subset {\mathbb R}^d, d \geq 3,$ odd, 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 $V(t) = e^{tG}, \: t \geq 0.$ In [10] we established that for $\gamma \equiv const$ and $K = \{x \in {\mathbb R}^3: \:|x| \leq 1\}$ the operator $G$ has no eigenvalues and we conjectured that the same result holds for every strictly convex obstacle. In this paper we prove this conjecture.
From: Vesselin Petkov [view email]
[v1]
Sat, 20 Jun 2026 09:13:52 UTC (16 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。