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The non-autonomous wave equation with general Wentzell boundary conditions

Published online by Cambridge University Press:  12 July 2007

Angelo Favini ,
Ciprian G. Gal ,
Gisèle Ruiz Goldstein ,
Jerome A. Goldstein  and
Silvia Romanelli
Angelo Favini
Affiliation:
Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy (favini@dm.unibo.it)
Ciprian G. Gal
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA (cgal@memphis.edu)
Gisèle Ruiz Goldstein
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA (ggoldste@memphis.edu)
Jerome A. Goldstein
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA (jgoldste@memphis.edu)
Silvia Romanelli
Affiliation:
Dipartimento di Matematica, Università degli Studi di Bari, via E. Orabona 4, 70125 Bari, Italy (romans@dm.uniba.it)
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Abstract

We study the problem of the well-posedness for the abstract Cauchy problem associated to the non-autonomous one-dimensional wave equation utt = A(t)u with general Wentzell boundary conditions Here A(t)u := (a(x, t)ux)x, a(x, t) ≥ ε > 0 in [0, 1] × [0, + ∞) and βj(t) > 0, γj(t) ≥ 0, (γ0(t), γ1(t)) ≠ (0,0). Under suitable regularity conditions on a, βj, γj we prove the well-posedness in a suitable (energy) Hilbert space

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 2 , April 2005 , pp. 317 - 329
Copyright
Copyright © Royal Society of Edinburgh 2005

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