Existence and uniqueness theorem for a class of singular nonlinear partial differential equations
type: Item
instance of: scholarly article
title: Existence and uniqueness theorem for a class of singular nonlinear partial differential equations
zbMATH Open document ID: 1258.35001
DOI: 10.2977/PRIMS/90
author: Dennis B. Bacani
author: Hidetoshi Tahara
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2013-01-17T00:00:00Z
review text: Summary: This paper deals with singular nonlinear partial differential equations of the form \(t\partial u/\partial t =F\left(t,x,u,\partial u/\partial x\right)\), with independent variables \((t,x)\in \mathbb{R}\times\mathbb{C}\), and where \(F(t,x,u,v)\) is a function continuous in \(t\) and holomorphic in the other variables. Using the Banach fixed point theorem (also known as the contraction mapping principle), we show that a unique solution \(u(t,x)\) exists under the condition that \(F(0,x,0,0)=0, F_u(0,x,0,0)=0\) and \(F_v(0,x,0,0)=x \gamma(x)\) with \(\text{Re}\, \gamma(0)<0\).
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A10
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 35A02
zbMATH DE Number: 6126566
zbMATH Keywords: nonlinear
zbMATH Keywords: partial differential equations
zbMATH Keywords: singular equations
zbMATH Keywords: existence and uniqueness of solutions
zbMATH Keywords: Banach fixed point theorem
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.2977/prims/90
OpenAlex ID: W2023426427
description: scientific article; zbMATH DE number 6126566