THE LAX-MIZOHATA THEOREM FOR NONLINEAR GAUZE INVARIANT EQUATIONS

摘要

We prove that ifthe Cauchy problem for the nonlinear partial differential equation is well-posed in a neighbourhood of a given solution, then all the characteristics of the equation are real-valued. For the linear equations this is a statement of the Lax-Mizohata theorem. Equations considered in the paper include gauge invariant localequations and systems, and non-local Kirchhoff type equations.