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arXiv · 2209.01735

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

Chong-Kyu Han·Taejung Kim
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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.

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Chong-Kyu Han, Taejung Kim. 2022-09-05. Maximal domains of solutions for analytic quasilinear differential equations of first order. https://arxiv.org/abs/2209.01735

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