Abstract
In this work, we establish a sufficient result for Exact null controllability of semilinear integro-differential system with non-autonomous functional evolution system. The results are obtained by using the Ascoli-Arzela theorem and Schauder fixed point theorem. An example is also provided to show an application of the obtained result.
Highlights
Controllability of linear and non-linear systems represented by ordinary differential equations in finite dimensional space has been extensively studied
We establish a sufficient result for Exact null controllability of semilinear integro-differential system with non-autonomous functional evolution system
We prove the exact null controllability of mild solution of the above integro-differential equation (1.1)
Summary
Controllability of linear and non-linear systems represented by ordinary differential equations in finite dimensional space has been extensively studied. Several authors have extended the concept to infinite dimensional systems represented by the evolution equations with bounded operators in Banach spaces [1, 2, 3, 4]. The study of controllability results for such systems in infinite dimensional space is important. Where A is the infintesimal generator of a strongly continuous semigroup S(s) in a Hilbert space Y , B is a linear bounded operator from a Hilbert space U into Y , F1 : J × Y → Y , F2 : J × C(W,Y ) → Y , the control function v(.) is given in L2(J,U).
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