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Preprints, Working Papers, ... Year : 2022

NULL CONTROLLABILITY OF STRONGLY DEGENERATE PARABOLIC EQUATIONS

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.
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hal-03789863 , version 1 (27-09-2022)

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Antoine Benoit, Romain Loyer, Lionel Rosier. NULL CONTROLLABILITY OF STRONGLY DEGENERATE PARABOLIC EQUATIONS. 2022. ⟨hal-03789863⟩
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