1. Generalized solutions of singular differential problems. Relationship with classical solutions
- Author
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Victor Dévoué, Jean-André Marti, Antoine Delcroix, Centre de recherches et de ressources en éducation et formation (CRREF), Université des Antilles et de la Guyane (UAG), Analyse Optimisation Controle (AOC), and Centre de Recherche en Economie, Gestion, Modélisation et Informatique Appliquée (CEREGMIA)
- Subjects
Generalized function ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Nonlinear generalized functions ,Regularization perspectives on support vector machines ,Nonlinear problems ,Wave equation ,[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] ,01 natural sciences ,Regularization (mathematics) ,010101 applied mathematics ,Nonlinear system ,Common point ,Singularity ,Singular solution ,Regularization of problems ,Applied mathematics ,Distributions ,0101 mathematics ,Regularization of data ,Analysis ,Characteristic problems ,Mathematics - Abstract
International audience; We discuss various methods of regularization of singular differential problems. Their common point is that we use the flexibility of the theories of nonlinear generalized functions for adapting the regularization to the singularity of the problem. We particularly underline the relationship between the generalized solutions and those classical or distribution, when they exist, giving a general result for the case of the regularization of data.
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