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http://dx.doi.org/10.4134/JKMS.j220043

MAXIMAL DOMAINS OF SOLUTIONS FOR ANALYTIC QUASILINEAR DIFFERENTIAL EQUATIONS OF FIRST ORDER

Han, Chong-Kyu (Research Institute of Mathematics Seoul National University)
Kim, Taejung (Department of Mathematical Education Korea National University of Education)

Publication Information

Journal of the Korean Mathematical Society / v.59, no.6, 2022 , pp. 1171-1184 More about this Journal

Abstract

We study the real-analytic continuation of local real-analytic solutions to the Cauchy problems of quasi-linear partial differential equations of first order for a scalar function. By making use of the first integrals 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.

Keywords

Real-analytic continuation; quasi-linear PDE of first order; first integrals; characteristic curves; scalar conservation laws;

Citations & Related Records

Reference

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