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Approximate controllability of a non-autonomous evolution equation in Banach spaces

  • * Corresponding author: Manil T. Mohan

    * Corresponding author: Manil T. Mohan 

The second author is supported by DST-INSPIRE Faculty Award (IFA17-MA110)

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  • In this paper, we consider a class of non-autonomous nonlinear evolution equations in separable reflexive Banach spaces. First, we consider a linear problem and establish the approximate controllability results by finding a feedback control with the help of an optimal control problem. We then establish the approximate controllability results for a semilinear differential equation in Banach spaces using the theory of linear evolution systems, properties of resolvent operator and Schauder's fixed point theorem. Finally, we provide an example of a non-autonomous, nonlinear diffusion equation in Banach spaces to validate the results we obtained.

    Mathematics Subject Classification: Primary: 34K06; Secondary: 34A12, 37L05, 93B05.


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