On singularly perturbed systems of ODE with a multiple root of the degenerate equation
Copyright policy )On singularly perturbed systems of ODE with a multiple root of the degenerate equation
Abstract We consider a boundary-value problem for a system of two second-order ODE with distinct powers of a small parameter at the second derivative in the first and second equations. When one of the two equations of the degenerate system has a double root, the asymptotic behaviour of the boundary-layer solution of the boundary-value problem turns out to be qualitatively different from the known asymptotic behaviour in the case when those equations have simple roots. In particular, the scales of the boundary-layer variables and the very algorithm for constructing the boundary-layer series depend on the type of the boundary conditions for the unknown functions. We construct and justify asymptotic expansions of the boundary-layer solution for boundary conditions of a particular type. These expansions differ from those for other boundary conditions.
Nonlinear boundary value problems for ordinary differential equations, case of multiple root of degenerate equation, Singular perturbations for ordinary differential equations, boundary layer, asymptotics in small parameter, Asymptotic expansions of solutions to ordinary differential equations, singularly perturbed boundary value problems
Nonlinear boundary value problems for ordinary differential equations, case of multiple root of degenerate equation, Singular perturbations for ordinary differential equations, boundary layer, asymptotics in small parameter, Asymptotic expansions of solutions to ordinary differential equations, singularly perturbed boundary value problems
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