Analysis and Control of Nonlinear Infinite Dimensional Systems

absolutely continuous accretive approximating assume assumptions Ay(t Banach space Barbu boundary value problem bounded subset Cauchy problem Chapter compact completes the proof convex function Corollary D(Aµ defined denoted duality mapping dx dt exists follows free boundary Gâteaux differentiable H¹(N H²(N Hamilton-Jacobi equations Hence Hilbert space implies L¹(N L²(N L²(Q Lemma lim inf lim sup linear locally Lipschitz lower semicontinuous m-accretive mild solution Moreover multiply Eq nonlinear norm obstacle problem optimal control optimal control problem optimal pair parabolic problem 1.1 proof of Theorem Proposition 1.1 readily seen semigroup Stefan problem strongly in H subdifferential tend to zero Theorem 1.1 u₁ uniformly convex unique solution variational inequalities Vt E 0,T weak star weakly x₁ y₁ y₂ yields Yn(t yo(x Ε Ω др ду