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October, 2020 Uniqueness of the solution of nonlinear singular first order partial differential equations
Hidetoshi TAHARA
J. Math. Soc. Japan 72(4): 1259-1282 (October, 2020). DOI: 10.2969/jmsj/82788278

Abstract

This paper deals with nonlinear singular partial differential equations of the form $t \partial u/\partial t = F(t,x,u,\partial u/\partial x)$ with independent variables $(t,x) \in \mathbb{R} \times \mathbb{C}$, where $F(t,x,u,v)$ is a function continuous in $t$ and holomorphic in the other variables. Under a very weak assumption we show the uniqueness of the solution of this equation. The results are applied to the problem of analytic continuation of local holomorphic solutions of equations of this type.

Funding Statement

This work was supported by JSPS KAKENHI Grant Number JP15K04966.

Citation

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Hidetoshi TAHARA. "Uniqueness of the solution of nonlinear singular first order partial differential equations." J. Math. Soc. Japan 72 (4) 1259 - 1282, October, 2020. https://doi.org/10.2969/jmsj/82788278

Information

Received: 27 May 2019; Published: October, 2020
First available in Project Euclid: 11 May 2020

MathSciNet: MR4165932
Digital Object Identifier: 10.2969/jmsj/82788278

Subjects:
Primary: 35A02
Secondary: 35B60, 35F20

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 4 • October, 2020
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