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.
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.