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Some PDEs problems in generalized Sobolev algebras

Séverine Andouze-Bernard 1 Silvère Nuiro 1
1 Analyse
LAMIA - Laboratoire de Mathématiques Informatique et Applications
Abstract : 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.
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Submitted on : Tuesday, April 3, 2012 - 6:42:05 PM
Last modification on : Friday, May 21, 2021 - 1:46:05 PM

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Séverine Andouze-Bernard, Silvère Nuiro. Some PDEs problems in generalized Sobolev algebras. Journal of Mathematical Analysis and Applications, Elsevier, 2012, 388, pp.647-658. ⟨10.1016/j.jmaa.2011.07.063⟩. ⟨hal-00685042⟩

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