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Uniqueness and approximation of solutions of first order nonlinear equations. (English) Zbl 0594.35018
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).
Reviewer: M.-T.Lacroix

MSC:
35F20 Nonlinear first-order PDEs
35A35 Theoretical approximation in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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