Advances in Difference Equations
Volume 2004 (2004), Issue 3, Pages 211-235
doi:10.1155/S1687183904401071
Rothe time-discretization method applied to a quasilinear wave equation subject to integral conditions
Département de Mathématiques, Centre Universitaire Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria
Received 27 January 2004; Revised 12 February 2004
Copyright © 2004 Abdelfatah Bouziani and Nabil Merazga. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper presents a well-posedness result for an initial-boundary
value problem with only integral conditions over the spatial domain
for a one-dimensional quasilinear wave equation. The solution and some
of its properties are obtained by means of a suitable application of
the Rothe time-discretization method.