Electron. J. Diff. Equ., Vol. 2014 (2014), No. 26, pp. 1-16.

Relaxation in control systems of fractional semilinear evolution equations

Xiaoyou Liu, Xi Fu

We consider a control system described by fractional semilinear evolution equations with a mixed multivalued control constraint whose values are nonconvex closed sets. Along with the original system, we consider the system in which the constraint on the control is the closed convex hull of the original constraint. We obtain existence results for the control systems and study relations between the solution sets of the two systems. An example is given to illustrate the abstract results.

Submitted October 15, 2013. Published January 14, 2014.
Math Subject Classifications: 34G20, 93C20, 34A08.
Key Words: Fractional semilinear evolution equation; relaxation property; feedback control; nonconvex constraint; mild solution.

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Xiaoyou Liu
School of Mathematics and Physics
University of South China
Hengyang 421001, Hunan Province, China
email: liuxiaoyou2002@hotmail.com Phone +86 13548962352
Xi Fu
Department of Mathematics, Shaoxing University
Shaoxing 312000, Zhejiang Province, China
email: fuxi1984@hotmail.com

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