Orrù, Nicola On a weakly hyperbolic equation with a term of order zero. (English) Zbl 0895.35057 Ann. Fac. Sci. Toulouse, VI. Sér., Math. 6, No. 3, 525-534 (1997). Summary: We study a weakly hyperbolic equation of second order, supposing that the coefficients of the principal part are analytic and depend only on time. We prove that if we add a term of order zero \(c(t,x)u\), with \(c\in C(\mathbb{R}^{n+1})\), the Cauchy problem remains well-posed in \(C^\infty\). Cited in 3 Documents MSC: 35L15 Initial value problems for second-order hyperbolic equations Keywords:well posed Cauchy problem × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] Colombini, F.), De Giorgi, E.) and Spagnolo, S.) .- Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps, Ann. Scuola Norm. Sup. Pisa, 6 (1979), pp. 511-559. · Zbl 0417.35049 [2] Colombini, F.), Jannelli, E.) and Spagnolo, S.) .- Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time, Ann. Scuola Norm. Sup. Pisa, 10 (1983), pp. 291-312. · Zbl 0543.35056 [3] Hörmander, L.) .- Linear Partial Differential Operators, Springer, Berlin (1963). · Zbl 0108.09301 [4] Kajitani, K.) .- The well posed Cauchy problem for hyperbolic operators, Exposé au Séminaire Vaillant (1989). [5] Oleinik, O.A.) .- On the Cauchy problem for weakly hyperbolic equations of second order, Comm. Pure Appl. Math.23 (1970), pp. 569-586. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.