Hyperbolicity of two by two systems with two independent variables

Tatsuo Nishitani
1998 Communications in Partial Differential Equations  
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
more » ... hyperbolic systems which includes a fortiori symmetrizable systems.
doi:10.1080/03605309808821378 fatcat:m3if4i7bojh2jci6rvd5seawei