一类具有瞬时脉冲的二阶发展方程的近似可控性

Abstract

Abstract:

In this paper, we study the approximate controllability for a class of second-order neutral evolution matrixs with infinite delay and instantaneous pulses in Hilbert spaces. The representation of mild solution of this matrix is obtained by using the cosine family theory, and combined with Schauder fixed point theorem, the existence conclusion of mild solution is obtained. By constructing an appropriate control function and using the resolvent operator type condition, the sufficient condition for the approximate controllability of this matrix is acquired. Finally, an example is given to illustrate the application of the main conclusions.

Key words: Approximate controllability, Second-order neutral evolution matrix, Infinite time delay, Instantaneous impulse, Cosine family theory

CLC Number:

O175.29

Kang Xiaodong, Fan Hongxia. Approximate Controllability for a Class of Second-Order Evolution Equations with Instantaneous Impulse[J].Acta mathematica scientia,Series A, 2023, 43(2): 421-432.

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Approximate Controllability for a Class of Second-Order Evolution Equations with Instantaneous Impulse

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