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Damped wave equations with dynamic boundary conditions

Mugnolo D.

Journal of Applied Analysis

2011

Vol. 17, nr 2

241-275

We discuss several classes of linear second order initial-boundary value problems in which damping terms appear in the main wave equation and/or in the dynamic boundary condition. We investigate their well-posedness and describe some qualitative properties of their solutions, like boundedness and stability. In particular, we provide sufficient conditions for analyticity, boundedness, asymptotic almost periodicity and exponential stability of certain C 0-semigroups associated to such problems.