Subdifferential Evolution Inclusion in Nonconvex Analysis

Under quite general assumptions, we prove existence, uniqueness and regularity of a solution U to the evolution equation U'(t) + (g F)(U(t)) 0, U(0)=u₀, where g : X {} is a closed convex proper function, F : Y X is a continuously differentiable mapping whose Jacobian is locally Lipschitz continuous, X and Y being two Hilbert spaces. We also study the stability and the asymptotic behavior of U, and give various examples.