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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2022; 59(6): 1171-1184

Online first article October 6, 2022      Printed November 1, 2022

https://doi.org/10.4134/JKMS.j220043

Copyright © The Korean Mathematical Society.

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

Chong-Kyu Han, Taejung Kim

Seoul National University; Korea National University of Education

Abstract

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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

MSC numbers: Primary 35F25, 35L67; Secondary 32K15, 58C15

Supported by: The authors were supported by NRF-Republic of Korea with grants 0450-20210049 (C.-K. Han) and 2018R1D1A3B07043346 (T. Kim), respectively.

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