K. Ravikumar, M. T. Mohan, A. Anguraj
Published 2020-04-22Version 1
In this paper, we consider a non-autonomus 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.
Approximate controllability of non-instantaneous impulsive fractional evolution equations of order $1<α<2$ with state-dependent delay in Banach spaces
Metric subregularity of the convex subdifferential in Banach spaces
Necessary optimality conditions for optimal control problems with nonsmooth mixed state and control constraints
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