Null controllability of strongly degenerate parabolic equations

Université du Littoral Côte d’Opale, Laboratoire de Mathématiques Pures et Appliquées J. Liouville, B.P. 699, 62228 Calais, France

^* Corresponding author: lionel.rosier@univ-littoral.fr

Received: 27 September 2022
Accepted: 8 March 2023

Abstract

We consider linear one-dimensional strongly degenerate parabolic equations with measurable coefficients that may be degenerate or singular. Taking 0 as the point where the strong degeneracy occurs, we assume that the coefficient a = a(x) in the principal part of the parabolic equation is such that the function x → x/a(x) is in L^p(0,1) for some p > 1. After establishing some spectral estimates for the corresponding elliptic problem, we prove that the parabolic equation is null controllable in the energy space by using one boundary control.