Well-posedness of characteristic symmetric hyperbolic systems.

*(English)*Zbl 0857.35080Summary: We consider the initial-boundary-value problem for quasilinear symmetric hyperbolic systems with characteristic boundary of constant multiplicity. We show well-posedness in Hadamard’s sense (i.e., existence, uniqueness and continuous dependence of solutions on the data) of regular solutions in suitable function spaces, which take into account the loss of regularity in the normal direction to the characteristic boundary.

##### MSC:

35L60 | First-order nonlinear hyperbolic equations |

35L50 | Initial-boundary value problems for first-order hyperbolic systems |

##### Keywords:

initial-boundary-value problem; quasilinear symmetric hyperbolic systems; characteristic boundary of constant multiplicity; well-posedness
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\textit{P. Secchi}, Arch. Ration. Mech. Anal. 134, No. 2, 155--197 (1996; Zbl 0857.35080)

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