Nash-Stackelberg controllability for coupled systems of degenerate equations in non-cylindrical domains

TL;DR

This paper establishes hierarchical null controllability for coupled degenerate semilinear parabolic equations in moving domains, employing Carleman estimates and inverse function theorem techniques.

Contribution

It introduces a novel approach to control coupled degenerate systems in non-cylindrical domains using adapted Carleman estimates.

Findings

Proves local null controllability of the system.

Develops a new Carleman estimate for degenerate non-autonomous equations.

Successfully applies inverse function theorem to nonlinear system.

Abstract

In this paper we investigate the Hierarchical null controllability of a coupled degenerate semilinear parabolic equation in domains which are moving in time. We show the local null controllability of the semilinear system using Liusternik's inverse function theorem. Nevertheless, the main difficulty is to adapt a Carleman estimate for the controllability of the linearized otimality system, using a Carleman inequality for degenerate non-autonomous equation obtanied by the authors previously.