Explicit boundary control of a reaction-diffusion equation on a disk

Abstract

This paper introduces an explicit full-state boundary feedback law that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on a disk. The backstepping method is used to design the control law. To apply backstepping the system is reduced to an infinite sequence of 1-D systems using Fourier series. H2 well-posedness and stability are proved, which implies that the solution is at least continuous on the disk.