Null controllability of degenerate heat equations

By Piermarco Cannarsa, Patrick S. Martinez, Judith Vancostenoble. Advances in Differential Equations, 2005

184 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aeb6415d6aacd0632a36432f3404b4c0f896d537

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Citations in the corpus

DEGENERATE PARABOLIC OPERATORS OF KOLMOGOROV TYPE WITH A GEOMETRIC CONTROL CONDITION (2015, background): “Then, null controllability holds if and only if γ ∈ (0, 1) [22, 23], while, for γ ≥ 1, the best result one can obtain is the so called regional null controllability [21], which consists in controlling the solution within the domain of in uence of the control.”
2d Grushin-type equations: Minimal time and null controllable data (2015, background): “In particular, null controllability still holds for weak degeneracies and fails for too strong ones, see [12, 13, 11, 1, 29, 10, 9, 8, 20, 34].”
CONTROLLABILITY OF 1-D COUPLED DEGENERATE PARABOLIC EQUATIONS (2009, methodology): “This inequality was basically proved in [6, 1, 8].”
Null controllability of Grushin-type operators in dimension two (2011, background): “Then it can be proved that null controllability holds if and only if γ ∈ (0, 1) (see [12, 13]), while, for γ ≥ 1, the best result one can show is “regional null controllability” (see [11]), which consists in controlling the solution within the domain of influence of the control.”
Controllability and Observability of Partial Differential Equations: Some Results and Open Problems (2007, result): “We refer to [23] for the first results in this direction, concerning the 1− d linear heat equation with a space-dependent coefficient degenerating on a single point, in a polynomial way.”
Null-controllability of hypoelliptic quadratic differential equations (2016, unknown): “This feature is well understood for parabolic equations that degenerate on the domain boundary, see [1, 8, 9, 10, 11, 39] in the one-dimensional case, and [12] for the multi-dimensional one.”
Improved Hardy-Poincaré inequalities and sharp Carleman estimates for degenerate/singular parabolic problems (2010, background): “We refer to [14] for the proof of the second characterization of D(A0).”