Dynamics of Partial Differential Equations
Volume 20 (2023)
Analyticity of the semigroup corresponding to a strongly damped wave equation with a Ventcel boundary condition
Pages: 249 – 262
We consider a wave equation with a structural damping coupled with an undamped wave equation located at its boundary. We prove that, due to the coupling, the full system is parabolic. In order to show that the underlying operator generates an analytical semigroup, we study in particular the effect of the damping of the “interior” wave equation on the “boundary” wave equation and show that it generates a structural damping.
analytic semigroups, structurally damped wave equation, Ventcel boundary condition
2010 Mathematics Subject Classification
35B65, 35K90, 35L05
The authors were partially supported by the ANR Grant “TRECOS” (ANR-20-CE40-0009).
Received 23 September 2022
Published 19 May 2023