Abstract
We consider the initial-boundary-value problem for quasi-linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity. We show the well-posedness in Hadamard's sense (i.e., existence, uniqueness and continuous dependence of solutions on the data) of regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary.
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Communicated by T.-P. Liu
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Secchi, P. Well-posedness of characteristic symmetric hyperbolic systems. Arch. Rational Mech. Anal. 134, 155–197 (1996). https://doi.org/10.1007/BF00379552
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DOI: https://doi.org/10.1007/BF00379552