Implicit differential equations with impasse singularities and singular perturbation problems
The authors study quasi-linear autonomous implicit ordinary differential equations (or shortly constrained systems) with an impasse manifold of codimension \(1\). The main results of the article are two theorems. The first one relates the orbits of a one-parameter family of constrained systems with those of a singular perturbation problem. The second one adapts the invariant manifold theorem of Fenichel to constrained systems. Finally, the authors study the case where the impasse surface is not regular. They show that under two hypotheses, a polar blowup leads to an equivalent constrained system with a regular impasse surface.
scientific article; zbMATH DE number 6105474