Topology on asymptotic algebras of generalized functions and applications
Nonlinear problems with singular coefficients or with singular additional conditions require the algebras of generalized functions. The authors of this paper construct such algebras of Colombeau type (called asymptotic algebras) starting from a locally convex metrizable topological space and using an asymptotic scale. A Hausdorff topology (called sharp topology) is defined in such an algebra. They also introduce temperate nonlinear mappings between them. Topological properties and the continuity of operations in such algebras have been analyzed. At the end, the authors treat a semilinear elliptic Dirichlet problem as an application of these algebras.
nonlinear problems with singular coefficients
scientific article; zbMATH DE number 1417251