Advances in Difference Equations
Volume 2004 (2004), Issue 3, Pages 211-235

Rothe time-discretization method applied to a quasilinear wave equation subject to integral conditions

Abdelfatah Bouziani and Nabil Merazga

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.


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.