Abstract and Applied Analysis
Volume 2009 (2009), Article ID 182371, 15 pages
doi:10.1155/2009/182371
Review Article

Well-Posedness of the Cauchy Problem for Hyperbolic Equations with Non-Lipschitz Coefficients

Akbar B. Aliev and Gulnara D. Shukurova

Baku State University, Academic Zahid Xalilov str., 23, AZ 1148 Baku, Azerbaijan

Received 12 March 2009; Accepted 16 May 2009

Academic Editor: Pavel Sobolevskii

Copyright © 2009 Akbar B. Aliev and Gulnara D. Shukurova. 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

We consider hyperbolic equations with anisotropic elliptic part and some non-Lipschitz coefficients. We prove well-posedness of the corresponding Cauchy problem in some functional spaces. These functional spaces have finite smoothness with respect to variables corresponding to regular coefficients and infinite smoothness with respect to variables corresponding to singular coefficients.