APPROXIMATE CONTROLLABILITY OF SECOND-ORDER SEMILINEAR EVOLUTION SYSTEMS WITH STATE-DEPENDENT INFINITE DELAY | Zendy

Xiaofeng Su | Zendy; Xianlong Fu | Zendy

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APPROXIMATE CONTROLLABILITY OF SECOND-ORDER SEMILINEAR EVOLUTION SYSTEMS WITH STATE-DEPENDENT INFINITE DELAY

Author(s) -

Xiaofeng Su,

Xianlong Fu

Publication year - 2020

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/20190217

Subject(s) - controllability , mathematics , resolvent , class (philosophy) , state (computer science) , trigonometric functions , first order , control theory (sociology) , order (exchange) , pure mathematics , control (management) , computer science , algorithm , finance , artificial intelligence , economics , geometry

In this article, we study the problem of approximate controllability for a class of semilinear second-order control systems with state-dependent delay. We establish some sufficient conditions for approximate controllability for this kind of systems by constructing fundamental solutions and using the resolvent condition and techniques on cosine family of linear operators. Particularly, theory of fractional power operators for cosine families is also applied to discuss the problem so that the obtained results can be applied to the systems involving derivatives of spatial variables. To illustrate the applications of the obtained results, two examples are presented in the end.

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