Persistent regional null contrillability for a class of degenerate parabolic equations

By Piermarco Cannarsa, Patrick S. Martinez, Judith Vancostenoble. 2004

113 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/6ba053a654d0c69c815e06420e89ce1bfbe92881

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Piermarco Cannarsa
2. Karine Beauchard
3. Luz de Teresa
4. Genni Fragnelli
5. Fatiha Alabau-Boussouira
6. Judith Vancostenoble
7. Dario Rocchetti
8. Luc Miller

In Control and Systems Engineering

1. Karine Beauchard
2. Piermarco Cannarsa
3. Luz de Teresa
4. Genni Fragnelli
5. Fatiha Alabau-Boussouira
6. Judith Vancostenoble
7. Dario Rocchetti
8. Luc Miller

In Mathematical Physics

1. Piermarco Cannarsa
2. Karine Beauchard
3. Genni Fragnelli
4. Luz de Teresa
5. Fatiha Alabau-Boussouira
6. Judith Vancostenoble
7. Dario Rocchetti
8. Luc Miller

Citations in the corpus

• CONTROLLABILITY OF 1-D COUPLED DEGENERATE PARABOLIC EQUATIONS (2009, unknown): “, [7]) that D(A) = {u ∈ H(1) a(0, 1) : aux ∈ H(1)(0, 1)} .”
• Regional controllability of semilinear degenerate parabolic equations in bounded domains (2006, methodology): “(see [5] for the well-posedness of such problem in C([0,1]); see also the Appendix of [ 8 ]).”
• Carleman estimates for degenerate parabolic operators with applications to null controllability (2006, background): “(see [5] for the well-possedness of such problem in C([0, 1]); see also the Appendix of [ 9 ]).”
• Carleman estimates for degenerate parabolic equations with first order terms and applications (2010, background): “…properties of linear one-dimensional degenerate parabolic equations with zero order terms are nowadays well known; see for instance [1,6,12,7] In [5] the authors study the property of null controllability of the system (4) with first order terms when the coefficient c only depends on…”
• Controllability results for a class of one-dimensional degenerate parabolic problems in nondivergence form (2008, result): “Using a result of Escauriaza, Seregin and Sverak (see [12] or [13]), that generalizes previous work by Micu and Zuazua (see [26] or [27]), we deduce, as in [ 7 ], that (4.7) is not null controllable.”
• 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].”
• 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.”