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Approximate controllability for impulsive neutral semilinear evolution equations with nonlocal conditions

Abstract:

The primary goal of this work is to establish the approximate controllability of a semilinear neutral-type system with nonlocal conditions and impulses, demonstrating that the approximate controllability of a neutral linear equation is preserved when external forces, impulses and nonlocal conditions are introduced as perturbations to the system. The approach leverages the properties of sectorial operators, the compactness of the semigroup that governs the evolution of the linear part of the equation and Rothe's fixed point theorem. To demonstrate the practical applicability of our method, we present a specific case that encompasses a broad family of examples, including a neutral-type heat equation.