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Approximate controllability of a non-autonomous evolution equation in Banach spaces
In this paper, we consider a non-autonomous nonlinear evolution equation 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