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

Well-posedness of the Cauchy problem for hyperbolic equations with non-Lipschitz coefficients

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.