Internal Layer for a Singularly Perturbed Equation with Discontinuous Right-Hand Sideстатья
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Дата последнего поиска статьи во внешних источниках: 16 декабря 2020 г.
Аннотация:We consider a boundary value problem for an ordinary singularly perturbed secondorder differential equation whose right-hand side is a nonlinear function with a discontinuityalong some curve that is independent of the small parameter. For this problem, we study theexistence of a smooth solution with steep gradient in a neighborhood of some point lying on thiscurve. The point itself and an asymptotic representation for the solution are to be determined.The existence theorem is proved by the method of matching asymptotic expansions. To this end,we use theorems on existence of solutions of boundary value problems for singularly perturbedequations and methods for constructing asymptotic approximations to these solutions.