. Proof, Note first that this result is a direct consequence of Definition A.1.1 if G is a Lipschitz-continuous function. Then, the lemma holds by using a sequence (G n ) of Lipschitz-continuous functions that converges uniformly to

. Au, espace, nous proposons une approximation de la température au front en dimension deux d'espace par une technique de changement d'inconnue. Pour la preuve de la monotonie de notre schéma, il nous a fallu définir une notion de 'propagation monotone' liée au mouvement du front pour pouvoir assurer l'existence de la température discrète au front. Malgré que ce travail se concentre essentiellement sur l'analyse numérique, cette partie de la thèse nous a donné un large aperçu des difficultés et certaines techniques caractéristiques de l'étude des problèmes à frontière libre. Nous espérons continuer ce travail sur le plan numérique en essayant par exemple d'autre méthode de discrétisation tel que la méthode des volumes finis utilisée dans la première partie et aussi prouver des résultats de convergence de la suite des solutions. Cette partie du travail est une suite d'un récent travail de N. Alibaud et G. Namah, qui ont démontré l'existence de solution onde

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