Second-order evolution problems with time-dependent maximal monotone operator and applications (Q1626429)

The authors study the unique existence of \(W_H^{2,\infty}([0,T], dt)\) solutions for a second-order evolution inclusion using a known result on first order differential inclusions in [\textit{D. Azzam-Laouir} et al., Set-Valued Var. Anal. 26, No. 3, 693--728 (2018; Zbl 1403.34046)]. They then derive some interesting results by applying the above existence theorem. In particular, they investigate several applications in optimal control in a new setting, including the Bolza relaxation problem, dynamic programming principle, viscosity in evolution inclusions driven by Lipschitz variation maximal monotone operators with Lipschitz perturbation and Young measure control, which have important applications in economics and mechanics. For the entire collection see [Zbl 1403.91012].