Approximate Controllability for a Class of Semilinear Abstract Equations

Zhou, Hong

doi:10.1137/0321033

Cited by 138 publications

(45 citation statements)

References 7 publications

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“…On the other hand, the notion of controllability plays a central role in the study of the theory of control and optimization. Therefore, there are a lot of works on the controllability, approximate controllability, and optimal control of linear and nonlinear differential and integral systems in various frameworks (see [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability for Functional Equations with Riemann-Liouville Derivative by Iterative and Approximate Method

Ibrahim

Fan

2017

Journal of Function Spaces

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We discuss the functional control systems governed by differential equations with Riemann-Liouville fractional derivative in general Banach spaces in the present paper. First we derive the uniqueness and existence of mild solutions for functional differential equations by the approach of fixed point and fractional resolvent under more general settings. Then we present new sufficient conditions for approximate controllability of functional control system by means of the iterative and approximate method. Our results unify and generalize some previous works on this topic.

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Section: Introductionmentioning

confidence: 99%

Approximate Controllability for Functional Equations with Riemann-Liouville Derivative by Iterative and Approximate Method

Ibrahim

Fan

2017

Journal of Function Spaces

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“…We consider the semilinear heat equation dealt with by Zhou [9], and Naito [4]. Let Then f is not uniformly bounded and R(g) ⊂ R(B) and from Theorem 3.2 it follows that the system of (SE1) is approximately controllable.…”

Section: S(t − S)f (S Y(s) V(s))dsmentioning

confidence: 99%

“…As for the some considerations on the trajectory set of (SE) and that of its corresponding linear system (in case f ≡ 0) as matters connected with (1), we refer to [8,9] and references therein.…”

Section: K(t − S)g(s X(s) U(s))dsmentioning

confidence: 99%

Controllability for Semilinear Functional Integrodifferential Equations

Jeong¹,

Kim²

2009

Bulletin of the Korean Mathematical Society

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Abstract. This paper deals with the regularity properties for a class of semilinear integrodifferential functional differential equations. It is shown the relation between the reachable set of the semilinear system and that of its corresponding linear system. We also show that the Lipschitz continuity and the uniform boundedness of the nonlinear term can be considerably weakened. Finally, a simple example to which our main result can be applied is given.

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“…Thereafter, based on the regularity results for solutions of (SE), we intend to establish the approximate controllability for (SE). The controllability results for linear control systems have been proved by many authors, and several authors have extended these concepts to infinite dimensional semilinear system (see [6][7][8]). In recent years, as for the controllability for semilinear differential equations, Carrasco and Lebia [9] discussed sufficient conditions for approximate controllability of parabolic equations with delay, and Naito [10] and other authors [6][7][8]11] proved the approximate controllability under the range conditions of the controller B.…”

Section: Introductionmentioning

confidence: 99%