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Generalized solutions of singular differential problems. Relationship with classical solutions. (English) Zbl 1169.35319
Summary: 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.

MSC:
35G20 Nonlinear higher-order PDEs
46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
35A20 Analyticity in context of PDEs
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