Stability analysis for optimal control problems governed by semilinear evolution equation

In this paper, the stability of solutions of optimal control for the distributed parameter system governed by a semilinear evolution equation with compact control set in the space L1(0,T;E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L^{1}(0,T;E)$\end{document} is discussed. The stability results for optimal control problems with respect to the right-hand side functions are obtained by the theory of set-valued mapping and the definition of essential solutions for optimal control problems.