We shall show the Gevrey wellposedness of the Cauchy problem for the hyperbolic equations of third order with coefficients depending only on time. For the proof we use the suitable energy of the third order equations.
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Tamotu Kinoshita, Gevrey Wellposedness of the Cauchy Problem for the Hyperbolic Equations of Third Order with Coefficients Depending Only on Time. Publ. Res. Inst. Math. Sci. 34 (1998), no. 3, pp. 249–270DOI 10.2977/PRIMS/1195144695