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under some assumptions on {(f)(x), \l/(x)} in case of m ^ 5, which was extended in case of m ^ 3 by Y. Nonaka ([2]). On the other hand, concerning to linear problem, fully degenerate hyperbolic Cauchy problems are studied by the author ([3]). A "fully degenerate" operator in a domain means an operator degenerating only on the boundary which is a characteristic whose order of multiplicity is equal to the order of the operator. The aim of this paper is to prove a local existence theorem for a quasi-linear hyperbolic Cauchy problem:

publications of the research institute for mathematical sciences

Local existence theorems and blow-up of solutions for quasi-linear hyperbolic Cauchy problems in a domain with characteristic boundary generated by initial data