NEW EXPLORATION ON APPROXIMATE CONTROLLABILITY OF DAMPED ELASTIC BEAM SYSTEMS IN BANACH SPACES

This article mainly studies the existence and approximate controllability of mild solutions for a class of Volterra-Fredholm type integral-differential damped elastic beam systems in Banach spaces. Firstly, the existence of mild solutions was obtained using Banach fixed point theorem and operator semigroup theory. Secondly, we formalized and proved the sufficient conditions for the approximate controllability of our desired problem. To test the results of approximate controllability, we used sequence method without assuming that the corresponding linear system is approximately controllable. Finally, an example is given to illustrate the theory results.