In this article we give some results on perturbation theory of 2 x 2 block operator matrices on the product of Banach spaces. Furthermore, we investigate their M-essential spectra. Finally, we apply the obtained results to determine the M-essential spectra of two group transport operators with general boundary conditions in the Banach space Lp([-a, a] x [-1, 1]) x Lp([-a, a] x [-1, 1]), p ≥ 1 and a > 0.
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.
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