Uniqueness of the solution of nonlinear singular first order partial differential equations

Hidetoshi Tahara

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arXiv · 1908.08182

Uniqueness of the solution of nonlinear singular first order partial differential equations

Hidetoshi Tahara

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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.

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Hidetoshi Tahara. 2019-08-22. Uniqueness of the solution of nonlinear singular first order partial differential equations. https://arxiv.org/abs/1908.08182

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