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On the efficiency of a uniqueness theorem for systems of partial differential equations. (Italian) Zbl 0574.35064

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)
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