Orateur
Nicolas Vanspranghe
Description
Consider linear waves on a bounded domain in the following setting. One part of the boundary is governed by a coupled lower-dimensional wave equation (i.e., dynamic Ventcel/Wentzell boundary condition) and is subject to viscous damping. The other (possibly empty) part is left at rest. When the dynamic boundary geometrically controls the domain, we show that the total energy of classical solutions decays like 1/t. The proof relies on an analysis of high-frequency quasimodes, suitable boundary estimates obtained in different microlocal regimes, and a special decoupling argument. Optimality is assessed via an appropriate quasimode construction.
Ongoing work with Hugo Parada (Institut de Mathématiques de Toulouse).
