Hyperbolicity of two by two systems with two independent variables
Journées équations aux dérivées partielles (1998), article no. 10, 12 p.

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 strongly hyperbolic systems which includes a fortiori symmetrizable systems.

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     author = {Nishitani, Tatsuo},
     title = {Hyperbolicity of two by two systems with two independent variables},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {10},
     publisher = {Universit\'e de Nantes},
     year = {1998},
     zbl = {01808719},
     mrnumber = {2000k:35004},
     language = {en},
     url = {http://archive.numdam.org/item/JEDP_1998____A10_0/}
}
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Nishitani, Tatsuo. Hyperbolicity of two by two systems with two independent variables. Journées équations aux dérivées partielles (1998), article  no. 10, 12 p. http://archive.numdam.org/item/JEDP_1998____A10_0/

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