Structurally damped plate and wave equations with random point force in arbitrary space dimensions

Stabilization of the damped plate equation under general boundary conditions

We consider a damped plate equation on an open bounded subset of R^d, or a smooth manifold, with boundary, along with general boundary operators fulfilling the Lopatinskii-Sapiro condition. The damping term acts on a region without imposing a geometrical condition. We derive a resolvent estimate for the generator of the damped plate semigroup that yields a logarithmic decay of the energy of the solution to the plate equation. The resolvent estimate is a consequence of a Carleman inequality obtained for the bi-Laplace operator involving a spectral parameter under the considered boundary conditi…

具有幂律记忆的结构阻尼 $σ-$演化方程

Structurally damped $σ-$evolution equations with power-law memory

本文研究含幂律记忆的结构阻尼 $σ-$演化方程，通过 Caputo-Djrbashian 导数与 Riemann-Liouville 积分构造 Cauchy 问题解表示，并建立色散及 Strichartz 估计。