Weak and strong semigroups in structural acoustic Kirchhoff-Boussinesq interactions with boundary feedback

• Published in: Journal of Differential Equations Vol. 298; pp. 387 - 429
• Main Authors: Lasiecka, Irena, Rodrigues, José H.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.10.2021
• Subjects: Boundary dissipation; Kirchhoff-Boussinesq plate; Nonlinear hybrid semigroup; Structural acoustic interaction; secondary; Nonlinear hybrid semigroup; Kirchhoff-Boussinesq plate; Structural acoustic interaction; primary; Boundary dissipation
• ISSN: 0022-0396; 1090-2732
• DOI: 10.1016/j.jde.2021.07.009

We consider a structural-acoustic wall problem in three dimensions, in which the structural wall is modeled by a 2D Kirchhoff-Boussinesq plate and the acoustic medium is subject to boundary damping. For this model we study the existence of a continuous nonlinear semigroup associated with the model in the finite energy space. We show that strong/weak continuity of the semigroups depends on the support of the boundary damping. The complications are related to supercritical nonlinearity exhibited by the plate along with the compromised boundary regularity of the acoustic waves. Compensated compactness methods along with a hidden boundary regularity of hyperbolic traces are exploited in order to establish weak (resp. strong) generation of a nonlinear semigroup subjected to feedback forces placed on the boundary of the acoustic medium.