American Institute of Mathematical Sciences

Advanced
December  2007, 2(4): 695-715. doi: 10.3934/nhm.2007.2.695

Null controllability of degenerate parabolic operators with drift

Piermarco Cannarsa 1, , Genni Fragnelli 2, and  Dario Rocchetti 1,

1. 

Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy
2. 

Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Siena, Via Roma 56, 53100 Siena

Received  June 2007 Revised  September 2007 Published  September 2007

We give null controllability results for some degenerate parabolic equations in non divergence form with a drift term in one space dimension. In particular, the coefficient of the second order term may degenerate at the extreme points of the space domain. For this purpose, we obtain an observability inequality for the adjoint problem using suitable Carleman estimates.
Keywords: Carleman estimates, Degenerate parabolic equations, null controllability, Hardy type inequality.
Mathematics Subject Classification: Primary: 93B05, 93C20, 93B07; Secondary: 35K6.
Citation: Piermarco Cannarsa, Genni Fragnelli, Dario Rocchetti. Null controllability of degenerate parabolic operators with drift. Networks & Heterogeneous Media, 2007, 2 (4) : 695-715. doi: 10.3934/nhm.2007.2.695
[1]

Genni Fragnelli. Null controllability of degenerate parabolic equations in non divergence form via Carleman estimates. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 687-701. doi: 10.3934/dcdss.2013.6.687
[2]

El Mustapha Ait Ben Hassi, Farid Ammar khodja, Abdelkarim Hajjaj, Lahcen Maniar. Carleman Estimates and null controllability of coupled degenerate systems. Evolution Equations & Control Theory, 2013, 2 (3) : 441-459. doi: 10.3934/eect.2013.2.441
[3]

Judith Vancostenoble. Improved Hardy-Poincaré inequalities and sharp Carleman estimates for degenerate/singular parabolic problems. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 761-790. doi: 10.3934/dcdss.2011.4.761
[4]

J. Carmelo Flores, Luz De Teresa. Null controllability of one dimensional degenerate parabolic equations with first order terms. Discrete & Continuous Dynamical Systems - B, 2020, 25 (10) : 3963-3981. doi: 10.3934/dcdsb.2020136
[5]

Farid Ammar Khodja, Cherif Bouzidi, Cédric Dupaix, Lahcen Maniar. Null controllability of retarded parabolic equations. Mathematical Control & Related Fields, 2014, 4 (1) : 1-15. doi: 10.3934/mcrf.2014.4.1
[6]

Lahcen Maniar, Martin Meyries, Roland Schnaubelt. Null controllability for parabolic equations with dynamic boundary conditions. Evolution Equations & Control Theory, 2017, 6 (3) : 381-407. doi: 10.3934/eect.2017020
[7]

Lydia Ouaili. Minimal time of null controllability of two parabolic equations. Mathematical Control & Related Fields, 2020, 10 (1) : 89-112. doi: 10.3934/mcrf.2019031
[8]

Brahim Allal, Abdelkarim Hajjaj, Lahcen Maniar, Jawad Salhi. Null controllability for singular cascade systems of $ n $-coupled degenerate parabolic equations by one control force. Evolution Equations & Control Theory, 2021, 10 (3) : 545-573. doi: 10.3934/eect.2020080
[9]

Thuy N. T. Nguyen. Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and applications to controllability. Mathematical Control & Related Fields, 2014, 4 (2) : 203-259. doi: 10.3934/mcrf.2014.4.203
[10]

Enrique Fernández-Cara, Luz de Teresa. Null controllability of a cascade system of parabolic-hyperbolic equations. Discrete & Continuous Dynamical Systems, 2004, 11 (2&3) : 699-714. doi: 10.3934/dcds.2004.11.699
[11]

Lin Yan, Bin Wu. Null controllability for a class of stochastic singular parabolic equations with the convection term. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021182
[12]

Piermarco Cannarsa, Patrick Martinez, Judith Vancostenoble. Persistent regional null contrillability for a class of degenerate parabolic equations. Communications on Pure & Applied Analysis, 2004, 3 (4) : 607-635. doi: 10.3934/cpaa.2004.3.607
[13]

Morteza Fotouhi, Leila Salimi. Controllability results for a class of one dimensional degenerate/singular parabolic equations. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1415-1430. doi: 10.3934/cpaa.2013.12.1415
[14]

El Mustapha Ait Ben Hassi, Mohamed Fadili, Lahcen Maniar. Controllability of a system of degenerate parabolic equations with non-diagonalizable diffusion matrix. Mathematical Control & Related Fields, 2020, 10 (3) : 623-642. doi: 10.3934/mcrf.2020013
[15]

Brahim Allal, Abdelkarim Hajjaj, Jawad Salhi, Amine Sbai. Boundary controllability for a coupled system of degenerate/singular parabolic equations. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021055
[16]

Farid Ammar Khodja, Franz Chouly, Michel Duprez. Partial null controllability of parabolic linear systems. Mathematical Control & Related Fields, 2016, 6 (2) : 185-216. doi: 10.3934/mcrf.2016001
[17]

Enrique Fernández-Cara, Manuel González-Burgos, Luz de Teresa. Null-exact controllability of a semilinear cascade system of parabolic-hyperbolic equations. Communications on Pure & Applied Analysis, 2006, 5 (3) : 639-658. doi: 10.3934/cpaa.2006.5.639
[18]

Larbi Berrahmoune. Null controllability for distributed systems with time-varying constraint and applications to parabolic-like equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (8) : 3275-3303. doi: 10.3934/dcdsb.2020062
[19]

Emmanuele DiBenedetto, Ugo Gianazza and Vincenzo Vespri. Intrinsic Harnack estimates for nonnegative local solutions of degenerate parabolic equations. Electronic Research Announcements, 2006, 12: 95-99.

[20]

Sergio Polidoro, Annalaura Rebucci, Bianca Stroffolini. Schauder type estimates for degenerate Kolmogorov equations with Dini continuous coefficients. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2022023

2020 Impact Factor: 1.213

Tools

Metrics

  • PDF downloads (126)
  • HTML views (0)
  • Cited by (33)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy