Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-16T22:31:04.670Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)