Approximate controllability of a non-autonomous evolution equation in Banach spaces
K. Ravikumar, Manil T. Mohan, A. Anguraj
Abstract
<p style='text-indent:20px;'>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.
Topics & Concepts
ControllabilityBanach spaceMathematicsC0-semigroupFixed-point theoremNonlinear systemResolventSeparable spaceClass (philosophy)Banach manifoldMathematical analysisFinite-rank operatorEvolution equationPure mathematicsApplied mathematicsLp spaceComputer scienceQuantum mechanicsArtificial intelligencePhysicsStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis