Carleman estimates for the structurally damped plate equations with Robin boundary conditions and applications. Issue 13 (2nd September 2022) - Fu, Xiaoyu; Tian, Jiaxin
Abstract : In this paper, we consider Carleman estimates for the damped fourth-order plate operators ∂ t t − ρ ∂ t Δ + Δ 2 in a bounded smooth domain with Robin boundary conditions. Because the appearance of such kind of structural damping, the speed of propagation for solutions to the plate equation is infinite and the corresponding properties of the solution similar to heat equations, and is significantly different from that of the usual plate equations without damping. As applications, we consider two types of inverse problems in determining source terms for the plate equation with structural damping. The time-dependent measurements can be restricted to an arbitrary small sub-domain or arbitrary sub-boundary, respectively. Under some assumptions on the regularity of the solutions and coefficients, we prove the global stability results for these inverse problems.