Equivalence of minimal time and minimal norm control problems for semilinear heat equations

TL;DR

This paper proves the equivalence between minimal time and minimal norm control problems for semilinear heat equations with internal controls, and demonstrates the Bang-Bang property for minimal norm controls.

Contribution

It establishes the theoretical equivalence of two control problems and introduces the Bang-Bang property for minimal norm controls in semilinear heat equations.

Findings

Proved the equivalence of minimal time and minimal norm control problems.

Established the Bang-Bang property for minimal norm controls.

Applied the results to semilinear heat equations with internal controls.

Abstract

In this paper, we establish the equivalence of minimal time and minimal norm control problems for semilinear heat equations in which the controls are distributed internally in an open subset of the state domain. As an application, the Bang-Bang property for minimal norm controls are also presented.