Abstract
Nonlinear multivalued differential equations with slow and fast subsystems are considered. Under transitivity conditions on the fast subsystem, the slow subsystem can be approximated by an averaged multivalued differential equation. The approximation in the Hausdorff sense is of order O(ϵ1/3) as ϵ → 0.
Highlights
We consider the nonlinear perturbed multivalued differential equation z(t) ∈ F z(t), y(t), y(t) ∈ G y(t), (1.1)where > 0 denotes the small perturbation parameter, t ∈ [0, T / ] the time variable, z(·) the slow motion, and y(·) the fast motion.The fundamental task in perturbation theory is the construction of a limit system which represents the situation of a vanishing perturbation parameter.In the single-valued case, F (z, y) = {f (z, y)} and G(y) = {g(y)}, that is, in the case of perturbed ordinary differential equations, this construction requires ergodicity properties of the fast subsystem
One mainly has to know how fast the unique invariant measure can be realized by single trajectories, that is, how fast the unique invariant measure can be approximated by occupation measures
We focus on the fast subsystem y(t) ∈ G y(t), y(0) = y0 ∈ N
Summary
Nonlinear multivalued differential equations with slow and fast subsystems are considered. Under transitivity conditions on the fast subsystem, the slow subsystem can be approximated by an averaged multivalued differential equation. The approximation in the Hausdorff sense is of order O( 1/3) as → 0. 2000 Mathematics Subject Classification: 34A60, 34E15, 34C29
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
