Boundary controllability for a coupled system of degenerate/singular parabolic equations

TL;DR

This paper investigates boundary controllability of a coupled degenerate/singular parabolic system with control on one equation, providing controllability results and cost estimates using the moment method and biorthogonal families.

Contribution

It introduces new controllability results for coupled degenerate/singular parabolic systems with a single boundary control, including cost estimates.

Findings

Established approximate and null boundary controllability.

Derived estimates on null-control cost.

Applied the moment method and biorthogonal families in proofs.

Abstract

In this paper we study the boundary controllability for a system of two coupled degenerate/singular parabolic equations with a control acting on only one equation. We analyze both approximate and null boundary controllability properties. Besides, we provide an estimate on the null-control cost. The proofs are based on the use of the moment method by Fattorini and Russell together with some results on biorthogonal families.