Controllability of a system of non-autonomous degenerate coupled parabolic equations

TL;DR

This paper establishes a Carleman estimate for a degenerate parabolic equation with a time-dependent coefficient and demonstrates the null controllability of a coupled system with such operators, advancing control theory for complex PDEs.

Contribution

It introduces a novel Carleman estimate for a degenerate, non-autonomous parabolic equation and applies it to prove null controllability of a coupled system with similar properties.

Findings

Proved a Carleman estimate for a degenerate parabolic PDE with time-dependent coefficients.

Established null controllability for a coupled system involving such degenerate operators.

Extended control techniques to systems with degeneracy and non-autonomous features.

Abstract

We prove a Carleman estimate for a one-dimensional parabolic equation which degenerates at one extremity of the domain and has a bounded, time dependent coefficient multiplying the diffusion term. Then we use the estimate to show the null controllability of a coupled system characterized by this form of diffusion operator and bounded coefficients.