Acoustic wave motions stabilized by boundary memory damping. (July 2016)

• Record Type: Journal Article
• Authors: Jiao, Zhe; Xiao, Ti-Jun
• Is Part Of: Applied mathematics letters. Volume 57(2016:Jul.)
• Page Start: 82
• Page End: 89
• Publication Date: 2016-07
• Subjects: Wave equations -- Acoustic boundary conditions -- Boundary memory damping -- Semigroup method -- Strong stability; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2015.12.014
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We consider the linear wave equation with acoustic boundary conditions (ABC) on a portion Γ 1 of the boundary and Dirichlet conditions on the rest of the boundary. The ABC contain a damping term of memory type with respect to the normal displacement of the point of Γ 1 . Under some assumption on the memory kernel, we show that the associated operator matrix generates a strongly continuous semigroup of contractions on a Hilbert space, and the semigroup is strongly stable.