Éditeur(s) : HAL CCSD Résumé : To appear in TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS (16 pages). In the last two decades, many algebras of generalized functions have been constructed, particularly the so-called generalized Sobolev algebras. Our goal is to study the latter and some of their main properties. In this framework, we pose and solve a nonlinear degenerated Dirichlet problem with irregular data such as Dirac generalized functions. https://hal.archives-ouvertes.fr/hal-00004903
Éditeur(s) : HAL CCSDElsevier Résumé : International audience The aim of this paper is to prove that the framework of generalized functions of Sobolev type is more suitable to pose and solve some PDEs problems with very irregular data, than the one introduced by J.-F. Colombeau, when ${mathcal{C}}^{infty}$ estimates are not available or out of reach. In such type of algebras, one shows the existence and some qualitative properties of solutions for problems appearing in the mathematical modelisation of oil activities. Journal of Mathematical Analysis and applications
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