Abstract and Applied Analysis

Control Systems Described by a Class of Fractional Semilinear Evolution Equations and Their Relaxation Property

Xiaoyou Liu and Xi Fu

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Abstract

We consider a control system described by a class of fractional semilinear evolution equations in a separable reflexive Banach space. The constraint on the control is a multivalued map with nonconvex values which is lower semicontinuous with respect to the state variable. Along with the original system we also consider the system in which the constraint on the control is the upper semicontinuous convex-valued regularization of the original constraint. We obtain the existence results for the control systems and the relaxation property between the solution sets of these systems.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 850529, 20 pages.

Dates
First available in Project Euclid: 7 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1399487812

Digital Object Identifier
doi:10.1155/2012/850529

Mathematical Reviews number (MathSciNet)
MR3004937

Zentralblatt MATH identifier
1255.93071

Citation

Liu, Xiaoyou; Fu, Xi. Control Systems Described by a Class of Fractional Semilinear Evolution Equations and Their Relaxation Property. Abstr. Appl. Anal. 2012 (2012), Article ID 850529, 20 pages. doi:10.1155/2012/850529. https://projecteuclid.org/euclid.aaa/1399487812


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