The Boundary of an Integral Funnel of a Differential Inclusion

Abstract

In the theory of differential inclusions of the form where Φ (q, t) is, for every q and t, a given non-empty convex set in the event space { q, t), the set of points of absolutey continuous integral curves q = q (t), t ≥ t’, of (1) originating from the point {q’, t’) is known as the integral funnel with vertex {q’, t’) for the differential inclusion (1). If integral curves are considered on a time segment (t’, t1), one can speak of a segment of the integral funnel. A segment of the integral funnel, with vertex {q’, t’) for the differential inclusion (1) will be denoted by V (q’, t’, t₁). We shall examine the case where the segment V (q’, t’, t₁) has a “rigid” lateral boundary in the form of a conoid with vertex {q’, t’).