Strictly hyperbolic equations with nonregular coefficients with respect to time (Q2756114)

This paper is a short review of some previous papers by the same author [Ital. J. Pure Appl. Math. 4, 73-82 (1998; Zbl 0967.35087), Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 18, No. 1, 39-66 (1991; Zbl 0761.35055) and J. Partial Differ. Equations 10, No. 3, 284-288 (1997; Zbl 0890.35079)]. NEWLINENEWLINENEWLINEThree different topics related to strictly hyperbolic equations with non-Lipschitz-continuous coefficients are considered: the results of \textit{F. Colombini, E. De Giorgi} and \textit{S. Spagnolo} [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 6, 511-559 (1979; Zbl 0417.35049)] and those of \textit{F. Colombini} and \textit{N. Lerner} [Duke Math. J. 77, No.3, 657-698 (1995; Zbl 0840.35067)] on the \(C^\infty\)-well-posedness of second-order hyperbolic equations with log-Lipschitz-continuous coefficients are extended to some classes of first-order hyperbolic systems of pseudodifferential operators and to scalar operators of higher order. NEWLINENEWLINENEWLINEThe results of \textit{F. Colombini, E. De Giorgi} and \textit{S. Spagnolo} [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 6, 511-559 (1979; Zbl 0417.35049)] on the Gevrey well-posedness for second-order operators having Hölder-continuous coefficients are extended to the case of systems and higher-order operators. NEWLINENEWLINENEWLINEFinally some results on propagation of singularities for such kind of hyperbolic systems are given.