Feedback control for nonlinear evolutionary equations with applications. (August 2022)

• Record Type: Journal Article
• Authors: Zeng, Biao
• Is Part Of: Nonlinear analysis. Volume 66(2022)
• Publication Date: 2022-08
• Subjects: Nonlinear evolutionary equation -- Feedback control -- Weakly continuous operator -- Optimal control -- Existence; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103535
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In the paper we are concerned with the feedback control system governed by nonlinear evolutionary equations involving weakly continuous operators. By using the Rothe method and a surjectivity result for weakly continuous operators, we first present the solvability for the evolutionary equation. Then we show the existence of solutions to the feedback control system. We also consider an existence result for an optimal control problem. Moreover, we apply the main results to a class of differential variational inequalities, evolutionary hemivariational inequalities and the non-stationary Navier–Stokes–Voigt equation with a subgradient inclusion condition.