Asymptotic Stability of the Wave Equation on Compact Manifolds and Locally Distributed Damping: A Sharp Result

Uniform energy decay rates for nonlinear viscoelastic wave equation with nonlocal boundary damping

“…In the absence of memory term, we can see the results regarding the wave equation subject to damping and source terms in the classical papers [10][11][12][13][14][15]. Finally, in what concerns the purely wave equation subject to a localized dissipation, namely, b(x) ≥ β > 0 in some proper subset ω ⊂ Ω, we may refer [16][17][18][19].…”

Uniform Decay Rates for the Wave Equation with Nonlinear Damping Locally Distributed in Unbounded Domains with Finite Measure

“…Among the numerous works, we can mention the following ones: [ALA], [ALA2], [ALA3], [ACG], [ALA4], [BLR], [BRT], [CDCFS], Downloaded 01/05/15 to 129.2.19.100. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php [CDCFS2], [DLT], [CDCFT], [CHEN1], [CHEN2], [ELN], [LA-TO], [Liu], [LZ], [AN], [NP], [NP2], [NV], [MAR], [MAR2], [VM], [NA1], [NA2], [NA3], [T], [Z].…”

Uniform stabilization of wave equation with localized damping and acoustic boundary condition

“…The characteristic of these problems is that the damping is imposed only over a domain portion. We emphasize the works [3,5,6,9,7] where the authors explored geometric aspects of the domain.…”

“…Wave equation with internal localized damping has been extensively studied, see [3,5,6,9,7,21,29,33] and references therein. The characteristic of these problems is that the damping is imposed only over a domain portion.…”