Maximal domains of solutions for analytic quasilinear differential equations of first order
Analysis of PDEs
2022-09-09 v2 Complex Variables
Dynamical Systems
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
Cite
@article{arxiv.2209.01735,
title = {Maximal domains of solutions for analytic quasilinear differential equations of first order},
author = {Chong-Kyu Han and Taejung Kim},
journal= {arXiv preprint arXiv:2209.01735},
year = {2022}
}
Comments
Typos are fixed. It will appear in Journal of the Korean Mathematical Society