On a class of singular nonlinear first order partial differential equations

2020/10/04 by Hidetoshi Tahara, Tahara, Hidetoshi
Mathematics · #35F20 #Advanced Differential Equations and Dynamical Systems #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2010.01467

openalex publication_date 2020/10/04 · openalex created_date 2020/10/08 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider a class of singular nonlinear first order partial differential equations t(∂ u/∂ t)=F(t,x,u, ∂ u/∂ x) with (t,x) ∈ ℝ × ℂ under the assumption that F(t,x,z₁,z₂) is a function which is continuous in t and holomorphic in the other variables. Under suitable conditions, we determine all the solutions of this equation in a neighborhood of the origin.

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