Dynamics of Partial Differential Equations

Volume 20 (2023)

Number 3

Analyticity of the semigroup corresponding to a strongly damped wave equation with a Ventcel boundary condition

Pages: 249 – 262

DOI: https://dx.doi.org/10.4310/DPDE.2023.v20.n3.a5

Authors

Mehdi Badra (Université Paul Sabatier, Institut de Mathématiques de Toulouse, France)

Takéo Takahashi (Université de Lorraine, Nancy, France)

Abstract

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.

Keywords

analytic semigroups, structurally damped wave equation, Ventcel boundary condition

2010 Mathematics Subject Classification

35B65, 35K90, 35L05

Full Text (PDF format)

The authors were partially supported by the ANR Grant “TRECOS” (ANR-20-CE40-0009).

Received 23 September 2022

Published 19 May 2023