Null controllability of two kinds of coupled parabolic systems with switching control

TL;DR

This paper investigates the null controllability of coupled degenerate and non-degenerate parabolic systems with switching control, using spectral inequalities instead of Carleman estimates, and addresses controllability over segmented time intervals.

Contribution

It introduces a novel approach for null controllability of coupled systems with switching control using spectral inequalities, a departure from traditional Carleman estimate methods.

Findings

Established observability inequality for measurable time subsets.

Achieved null controllability via HUM method for coupled systems.

Extended controllability results to segmented time intervals.

Abstract

The focus of this paper is on the null controllability of two kinds of coupled systems including both degenerate and non-degenerate equations with switching control. We first establish the observability inequality for measurable subsets in time for such coupled system, and then by the HUM method to obtain the null controllability. Next, we investigate the null controllability of such coupled system for segmented time intervals. Notably, these results are obtained through spectral inequalities rather than using the method of Carleman estimates. Such coupled systems with switching control, to the best of our knowledge, are among the first to discuss.