Time dependent evolution inclusions governed by the difference of two subdifferentials

Sophie Guillaume (1)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon

The purpose of this paper is to study evolution inclusions involving time depen-dent subdifferential operators which are non-monotone. More precisely, we study existence of solutions for the following evolution equation in a real Hilbert space X : u ′ (t) + ∂f t (u(t)) − ∂ϕ t (u(t)) ∋ w(t), u(0) = u 0 , where f t and ϕ t are closed convex proper functions on X.

Mots clés: Convex and difference convex functions; Evolution inclusion; Subdifferential; local existence

Domaines: Optimisation et contrôle [math.OC]

Sophie Guillaume. Time dependent evolution inclusions governed by the difference of two subdifferentials. Electronic Journal of Qualitative Theory of Differential Equations, 2012, 92, pp.1 - 27. ⟨hal-01113748⟩