Propagation of analyticity of solutions to the Cauchy problem for Kirchhoff type equations

Kunihiko Kajitani

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Hyperbolicity of two by two systems with two independent variables

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We study the simplest system of partial differential equations: that is, two equations of first order partial differential equation with two independent variables with real analytic coefficients. We describe a necessary and sufficient condition for the Cauchy problem to the system to be C infinity well posed. The condition will be expressed by inclusion relations of the Newton polygons of some scalar functions attached to the system. In particular, we can give a characterization of the...