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On the solvability of the first mixed problem for strongly hyperbolic system in infinite nonsmooth cylinders. (English) Zbl 1178.35242
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 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.
MSC:
35L53Second-order hyperbolic systems, initial-boundary value problems
35D30Weak solutions of PDE