Using the abstract framework [Batkai, 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^{1,1}(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^{1,p}(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^{1,p}(0,1) for 1 < p < 1.

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

ENGEL, KLAUS JOCHEN OTTO;
2005-01-01

Abstract

Using the abstract framework [Batkai, 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^{1,1}(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^{1,p}(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^{1,p}(0,1) for 1 < p < 1.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/19143
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