On the solvability of the first mixed problem for strongly hyperbolic system in infinite nonsmooth cylinders (Q1022858)

A strongly hyperbolic system with homogeneous initial and boundary conditions on an infinite cylinder is considered. For the case of a finite cylinder see the paper of one of the author \textit{Nguyen Manh Hung} [Sb. Math. 190, No.~7, 1035--1058 (1999); translation from Mat. Sb. 190, No. 7, 103--126 (1999; Zbl 0962.35036)]. Under some specific conditions for the coefficients, one proves the existence and uniqueness of a generalized solution. The proof is based on Galerkin approximations and uses an extension of the Garding inequality.