Subdifferential evolution inclusion in nonconvex analysis
Existence, uniqueness and regularity of solutions to the evolution inclusion \(0\in U'(t)+ \partial(g\circ F)(U(t))\), \(U(0)= u_0\) are proved. Here \(g: X\to \mathbb{R}\cup\{\infty\}\) is a closed convex proper function with \(X\) a Hilbert space, \(F: Y\to X\) is a continuously differentiable mapping whose Jacobian is locally Lipschitz continuous, \(Y\) is another Hilbert space. Stability and asymptotic behavior of the solution are also given.
scientific article; zbMATH DE number 1545636