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. Dans-la-première-partie, nous étudions la décroissance auto-similaire de la solution d'une équation de renouvellement à queue lourde vers un état stationnaire

. Turée-en-Âge-et-À-sauts-en-espace, Nous y prouvons un résultat de stabilité : les solutions des problèmes rééchelonnés à ? > 0 convergent lorsque ? ? 0 vers la solution de viscosité de l'équation de Hamilton-Jacobi limite des problèmes à ? > 0

. Au-cours-de-cette-thèse, des simulations numériques de type Monte Carlo, schémas volumes nis, Lax-Friedrichs et Weighted Essentially Non Oscillating ont été réalisées

. Mots-clés, Analyse asymptotique, équations aux dérivées partielles, diusion anormale, équations structurées, entropie relative, équations de Hamilton-Jacobi, sous-diusion en biologie cel- lulaire