Abstract
We survey some known results about operator semigroup generated by operator matrices with diagonal or coupled domain. These abstract results are applied to the characterization of well-/ill-posedness for a class of evolution equations with dynamic boundary conditions on domains or metric graphs. In particular, our results on the heat equation with general Wentzell-type boundary conditions complement those previously obtained by, among others, Bandle–von Below–Reichel and Vázquez–Vitillaro.
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Mugnolo, D. Asymptotics of semigroups generated by operator matrices. Arab. J. Math. 3, 419–435 (2014). https://doi.org/10.1007/s40065-014-0107-4
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DOI: https://doi.org/10.1007/s40065-014-0107-4