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Cosine families generated by second-order differential operators on W(0, 1) with generalized Wentzell boundary conditions

Applicable Analysis, ISSN: 1563-504X, Vol: 84, Issue: 9, Page: 867-876
2005
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Article Description

Using the abstract framework [Bátkai, A. and Engel, K.-J., 2004, Abstract wave equations with generalized Wentzell boundary conditions. Journal of Differential Equations, 207, 1–20.] we show that certain second-order differential operators with generalized Wentzell boundary conditions generate cosine families and hence also analytic semigroups on W(0,1). This complements the main result [Favini, A., Ruiz Goldstein, G., Goldstein, J.A., Obrecht, E. and Romanelli, S., 2003, General Wentzell boundary conditions and analytic semigroups on W (0,1). Applicable Analysis, 82, 927–935.] on the generation of an analytic semigroup by the second derivative with generalized Wentzell boundary conditions on W (0, 1) for 1

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