Uniqueness and approximation of solutions of first order nonlinear equations
type: Item
instance of: scholarly article
title: Uniqueness and approximation of solutions of first order nonlinear equations
zbMATH Open document ID: 0594.35018
DOI: 10.1007/BF01388803
author: Guy Métivier
published in: Inventiones Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143286
review text: Soit \(\Omega =]0,T[\times \omega\), où \(\omega\) est un voisinage ouvert de 0 dans \({\mathbb{R}}^ N\), l'A. montre que toute solution de classe \(C^ 2\) du problème \[ (1)\quad \partial u/\partial t=F(t,x,u,\nabla u),\quad u(0,x)=\phi (u) \] est unique dans un voisinage de \(0\subset {\bar \Omega}\) (théorème 1.1.1). L'unicité dépend de l'approximation de u par une suite \(u_{\lambda}\in C^ 2(\Omega_ 0)\), où les \(u_{\lambda}\) sont solutions du problème (1) par une donnée initiale \(\phi_{\lambda}\) analytique, les \(u_{\lambda}\) étant également solution d'une équation implicite (lemme 2.3.1). Il faut de plus montrer que les \(u_{\lambda}\) sont définies sur un même voisinage \(\Omega_ 0\) de 0 (paragraphe 4).
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 3955516
zbMATH Keywords: nonlinear first order analytic partial differential equations
zbMATH Keywords: uniqueness of \(C^ 2\) complex valued solutions
zbMATH Keywords: noncharacteristic
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Hamiltonian field of the equation
reviewed by: Marie-Therese Lacroix
MaRDI profile type: Publication
cites work: Uniqueness in certain first-order nonlinear complex cauchy problems
cites work: Q3730699
cites work: A property of the functions and distributions annihilated by a locally integrable system of complex vector fields
cites work: Approximation of solutions of linear PDE with analytic coefficients
cites work: The Identity of Weak and Strong Extensions of Differential Operators
OpenAlex ID: W2035287167
description: scientific article; zbMATH DE number 3955516