Volume 29, 2023
|Number of page(s)||36|
|Published online||21 June 2023|
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: firstname.lastname@example.org
Accepted: 8 March 2023
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 Lp(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.
Mathematics Subject Classification: 35J25 / 35J70 / 35K65 / 35P15 / 93B05
Key words: Strongly degenerate parabolic equations / null controllability / measurable and singular coefficient / spectral estimates / flatness
© The authors. Published by EDP Sciences, SMAI 2023
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