A class of stochastic hyperbolic evolution equations via weighted pseudo almost periodic coefficients and optimal controls. (7th May 2019)

• Record Type: Journal Article
• Authors: Yan, Zuomao; Han, Li
• Is Part Of: Optimal control applications and methods. Volume 40:Number 5(2019)
• Page Start: 819
• Page End: 847
• Publication Date: 2019-05-07
• Subjects: evolution family -- fixed point -- impulsive stochastic hyperbolic evolution equations -- optimal controls -- piecewise weighted pseudo almost periodic functions; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2512
• Languages: English
• ISSNs: 0143-2087

Abstract

Summary: This paper introduces the concept of the piecewise weighted pseudo periodicity for stochastic processes. In addition, it establishes a new composition theorem for weighted pseudo almost periodic functions under the non‐Lipschitz conditions. Using this composition theorem, evolution family together with a fixed‐point theorem for condensing maps, we investigate the existence of p ‐mean piecewise weighted pseudo almost periodic mild solutions and optimal mild solutions for a class of impulsive stochastic hyperbolic evolution equations in Hilbert spaces. Then, the existence conditions of optimal pairs of systems governed by the nonlinear impulsive stochastic evolution equations are presented. Finally, an example is provided to illustrate the obtained theory.