Cinquini, Silvio On the efficiency of a uniqueness theorem for systems of partial differential equations. (Italian) Zbl 0574.35064 Rend., Sci. Mat. Appl., A 115(1981), 139-148 (1984). The author presents two examples to show that, in cases of more than two independent variables, the Cauchy problem for quasi-linear hyperbolic systems which are reducable to a given canonical form, admits a unique solution over a suitable domain. As indicated previously by the author [ibid. 114, 132-137 (1980; Zbl 0525.35053) and Atti. Accad. Sci. Ist. Bologna, Cl. Sci. Fis., Anno 268, Rend., XIII, Ser. 7, No.1, 123-132 (1980; Zbl 0508.35007)], a slightly different definition of hyperbolicity than Petrovski’s definition, insures the reducibility of the system to canonical form; this latter fact follows from standard matrix theory. Reviewer: R.Vaillancourt MSC: 35L75 Higher-order nonlinear hyperbolic equations 35L30 Initial value problems for higher-order hyperbolic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:Cauchy problem; quasi-linear hyperbolic systems; unique solution; canonical form Citations:Zbl 0525.35053; Zbl 0508.35007 PDFBibTeX XMLCite \textit{S. Cinquini}, Rend., Sci. Mat. Appl., A 115, 139--148 (1984; Zbl 0574.35064)