Well-posedness of the Cauchy problem for hyperbolic equations with non-Lipschitz coefficients. (English) Zbl 1176.35110

Summary: 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.


35L15 Initial value problems for second-order hyperbolic equations
35B65 Smoothness and regularity of solutions to PDEs
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