Local Solvability and Controllability of Semilinear Initial Value Control Problems via Semigroup Approach

Abstract

The aim of this paper is to prove the local existence, uniqueness and the exact controllability of the mild solutions of semilinear initial value control problems in suitable Banach spaces using semigroup theory "compact semigroup" and Schauder fixed point theorem.

Controllability of Nonlinear Boundary Value Control Systems in Banach Spaces Using Schauder Fixed Point Theorem

“…Since T(t), t > 0 is a compact , then T(t) is continuous in the uniform operator topology for t > 0. Thus the right -hand side of (10), which is independent of x∈Y 0 , tends to zero as tR 2 −R tR 1 R→ 0, so Φ(YR 0 R) is an equicontinuous family of functions.…”