Controllability results for a class of one-dimensional degenerate parabolic problems in nondivergence form

By Piermarco Cannarsa, Genni Fragnelli, Dario Rocchetti. 2008

104 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/0312506b01435defad8b1fd0578d1a516b7e494d

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. Karine Beauchard
2. Genni Fragnelli
3. Dimitri Mugnai
4. Piermarco Cannarsa
5. Roberto Guglielmi
6. Raphael Henry
7. Bernard Helffer
8. Luc Miller

In Control and Systems Engineering

1. Karine Beauchard
2. Genni Fragnelli
3. Dimitri Mugnai
4. Piermarco Cannarsa
5. Roberto Guglielmi
6. Bernard Helffer
7. Raphael Henry
8. Luc Miller

In Mathematical Physics

1. Karine Beauchard
2. Genni Fragnelli
3. Dimitri Mugnai
4. Piermarco Cannarsa
5. Luc Miller
6. Morgan Morancey
7. Roberto Guglielmi
8. Bernard Helffer

Citations in the corpus

• 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.”
• 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].”
• DEGENERATE PARABOLIC OPERATORS OF KOLMOGOROV TYPE WITH A GEOMETRIC CONTROL CONDITION (2015, background): “Several extensions of the above results are available in one space dimension, see [2, 49] for equations in divergence form, [20, 19] for operators in nondivergence form, and [18, 35] for cascade systems.”
• Null controllability of Grushin-type operators in dimension two (2011, background): “On the other hand, for γ ∈ (0, 1/2) we will follow the strategy of [1, 10, 37], adapting the weight β to the nonsmooth coefficient |x|2γ (see (78)–(79)).”
• Carleman estimates and observability inequalities for parabolic equations with interior degeneracy (2012, background): “A first example is their application to global null controllability (see [1], [2], [3], [4], [11], [12], [13], [18], [21], [22], [27], [28], [26], [29], [34] and the references therein): for all T > 0 and for all initial data u0 ∈ L((0, T )× (0, 1)) there is a suitable control h ∈ L((0, T )× (0, 1))”