Approximate controllability of a Sobolev type impulsive functional evolution system in Banach spaces | Zendy

Sumit Arora | Zendy; Manil T. Mohan | Zendy; Jaydev Dabas | Zendy

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Approximate controllability of a Sobolev type impulsive functional evolution system in Banach spaces

Author(s) -

Sumit Arora,

Manil T. Mohan,

Jaydev Dabas

Publication year - 2020

Publication title -

mathematical control and related fields

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.658

H-Index - 21

eISSN - 2156-8472

pISSN - 2156-8499

DOI - 10.3934/mcrf.2020049

Subject(s) - controllability , sobolev space , mathematics , banach space , type (biology) , pure mathematics , resolvent , fixed point theorem , sobolev inequality , mathematical analysis , c0 semigroup , ecology , biology

In this paper, we investigate the approximate controllability problems of certain Sobolev type differential equations. Here, we obtain sufficient conditions for the approximate controllability of a semilinear Sobolev type evolution system in Banach spaces. In order to establish the approximate controllability results of such a system, we have employed the resolvent operator condition and Schauder's fixed point theorem. Finally, we discuss a concrete example to illustrate the efficiency of the results obtained.

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