Maximal domains of solutions for analytic quasilinear differential equations of first order

Abstract

We study the real-analytic continuation of local real-analytic solutions to the Cauchy problems of quasi-linear partial differential equa-tions of first order for a scalar function. By making use of the first inte-grals of the characteristic vector field and the implicit function theorem we determine the maximal domain of the analytic extension of a local solution as a single-valued function. We present some examples including the scalar conservation laws that admit global first integrals so that our method is applicable.