On an Estimate Connected with the Stabilization of a Normal Parabolic Equation by Start Control

Abstract

After a brief revision of facts concerning semilinear parabolic equations of normal type and their nonlocal stabilization by start control, we provide a simplification of the proof of the lower bound for a functional of the solution to the heat equation with initial condition of a special type. This bound is essential to prove the nonlocal stabilization of equations of normal type. The simplification presented is required for further development of the nonlocal stabilization theory.