Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach

Authors : Luis Gerardo MÁRMOL, Carmen Judith VANEGAS

Pages : 113-125

Doi:10.33434/cams.446386

View : 24 | Download : 12

Publication Date : 2018-12-24

Article Type : Research Paper

Abstract :In this paper we study certain systems of mixed-type functional differential equations, from the point of view of the $C_{0}$-semigroup theory. In general, this type of equations are not well-posed as initial value problems. But there are also cases where a unique differentiable solution exists. For these cases and in order to achieve our goal, we first rewrite the system as a classical Cauchy problem in a suitable Banach space. Second, we introduce the associated semigroup and its infinitesimal generator and prove important properties of these operators. As an application, we use the results to characterize the null controllability for those systems, where the control $u$ is constrained to lie in a non-empty compact convex subset $\Om{}$ of $\R^n$.
Keywords : Functional differential equations, Strongly continuous semigroups, Mixed type difference differential equations, Exact controllability