%0 Journal Article
%T Projector Approach to Constructing Asymptotic Solution of Initial Value Problems for Singularly Perturbed Systems in Critical Case
%A Galina Kurina
%J -
%D 2019
%R https://doi.org/10.3390/axioms8020056
%X Abstract Under some conditions, an asymptotic solution containing boundary functions was constructed in a paper by VasilĄŻeva and Butuzov (Differ. Uravn. 1970, 6(4), 650¨C664 (in Russian); English transl.: Differential Equations 1971, 6, 499¨C510) for an initial value problem for weakly non-linear differential equations with a small parameter standing before the derivative, in the case of a singular matrix A ( t ) standing in front of the unknown function. In the present paper, the orthogonal projectors onto k e r A ( t ) and k e r A ( t ) Ąä (the prime denotes the transposition) are used for asymptotics construction. This approach essentially simplifies understanding of the algorithm of asymptotics construction. View Full-Tex
%K singular perturbations
%K initial value problems
%K asymptotics
%K critical case
%K projector approach
%U https://www.mdpi.com/2075-1680/8/2/56