On a class of algebras of generalized functions. Application to differential systems
In order to study partial differential equations having no distributional solutions, various algebras of generalized functions have been introduced [see e.g. the monograph of \textit{J. F. Colombeau}, ``Elementary introduction to new generalized functions'' (1985; Zbl 0584.46024) and a paper of \textit{Y. V. Egorov}, Russ. Math. Surveys 45, No. 5, 1-49 (1990; Zbl 0754.46034)]. In the paper under review, the author introduces, in terms of nonstandard analysis, yet another type of these algebras, called asymptotic algebras. Applications to differential problems are given.
partial differential equations having no distributional solutions
scientific article; zbMATH DE number 1053375