Impulse null approximate controllability for heat equation with dynamic boundary conditions

TL;DR

This paper establishes a logarithmic convexity estimate for solutions of a heat equation with dynamic boundary conditions and demonstrates impulsive null approximate controllability for such equations.

Contribution

It introduces a new logarithmic convexity estimate and applies it to prove impulsive null approximate controllability for heat equations with dynamic boundary conditions.

Findings

Logarithmic convexity estimate for heat equations with dynamic boundary conditions

Impulsive null approximate controllability established for impulsive heat equations

Method applicable to bounded convex domains

Abstract

The main purpose of this article is to prove a logarithmic convexity estimate for the solution of a linear heat equation subject to dynamic boundary conditions in a bounded convex domain. As an application, we prove the impulsive null approximate controllability for an impulsive heat equation with dynamic boundary conditions.