November  2006, 6(6): 1213-1238. doi: 10.3934/dcdsb.2006.6.1213

A geometric inverse problem for the Boussinesq system


Universidad de Sevilla, Dpto. E.D.A.N., Aptdo. 1160, 41080, Sevilla, Spain


Dpto., E.D.A.N., Universidad de Sevilla, Aptdo. 1180; 41080 Sevilla


Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla


Universidad del Bío-Bío, Dpto. de Ciencias Básicas, Casilla 447, Fernando May, Chillán, Chile

Received  November 2005 Revised  June 2006 Published  August 2006

In this work we present some results for the inverse problem of the identification of a single rigid body immersed in a fluid governed by the stationary Boussinesq equations. First, we establish a uniqueness result. Then, we show the way the observation depends on perturbations of the rigid body and we deduce some consequences. Finally, we present a new method for the partial identification of the body assuming that it can be deformed only through fields that, in some sense, are finite dimensional. In the proofs, we use various techniques, related to Carleman estimates, differentiation with respect to domains, data assimilation and controllability of PDEs.
Citation: A. Doubov, Enrique Fernández-Cara, Manuel González-Burgos, J. H. Ortega. A geometric inverse problem for the Boussinesq system. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1213-1238. doi: 10.3934/dcdsb.2006.6.1213

Alexandre J. Chorin, Fei Lu, Robert N. Miller, Matthias Morzfeld, Xuemin Tu. Sampling, feasibility, and priors in data assimilation. Discrete & Continuous Dynamical Systems, 2016, 36 (8) : 4227-4246. doi: 10.3934/dcds.2016.36.4227


Dugan Nina, Ademir Fernando Pazoto, Lionel Rosier. Controllability of a 1-D tank containing a fluid modeled by a Boussinesq system. Evolution Equations & Control Theory, 2013, 2 (2) : 379-402. doi: 10.3934/eect.2013.2.379


Jon Asier Bárcena-Petisco, Kévin Le Balc'h. Local null controllability of the penalized Boussinesq system with a reduced number of controls. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021038


Yuming Qin, Yang Wang, Xing Su, Jianlin Zhang. Global existence of solutions for the three-dimensional Boussinesq system with anisotropic data. Discrete & Continuous Dynamical Systems, 2016, 36 (3) : 1563-1581. doi: 10.3934/dcds.2016.36.1563


Pedro Caro. On an inverse problem in electromagnetism with local data: stability and uniqueness. Inverse Problems & Imaging, 2011, 5 (2) : 297-322. doi: 10.3934/ipi.2011.5.297


Victor Isakov. On uniqueness in the inverse conductivity problem with local data. Inverse Problems & Imaging, 2007, 1 (1) : 95-105. doi: 10.3934/ipi.2007.1.95


Débora A. F. Albanez, Maicon J. Benvenutti. Continuous data assimilation algorithm for simplified Bardina model. Evolution Equations & Control Theory, 2018, 7 (1) : 33-52. doi: 10.3934/eect.2018002


Jochen Bröcker. Existence and uniqueness for variational data assimilation in continuous time. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021050


Manuel González-Burgos, Sergio Guerrero, Jean Pierre Puel. Local exact controllability to the trajectories of the Boussinesq system via a fictitious control on the divergence equation. Communications on Pure & Applied Analysis, 2009, 8 (1) : 311-333. doi: 10.3934/cpaa.2009.8.311


Nicolás Carreño. Local controllability of the $N$-dimensional Boussinesq system with $N-1$ scalar controls in an arbitrary control domain. Mathematical Control & Related Fields, 2012, 2 (4) : 361-382. doi: 10.3934/mcrf.2012.2.361


Xiaoqiang Dai, Shaohua Chen. Global well-posedness for the Cauchy problem of generalized Boussinesq equations in the control problem regarding initial data. Discrete & Continuous Dynamical Systems - S, 2021, 14 (12) : 4201-4211. doi: 10.3934/dcdss.2021114


Suman Kumar Sahoo, Manmohan Vashisth. A partial data inverse problem for the convection-diffusion equation. Inverse Problems & Imaging, 2020, 14 (1) : 53-75. doi: 10.3934/ipi.2019063


Francis J. Chung. Partial data for the Neumann-Dirichlet magnetic Schrödinger inverse problem. Inverse Problems & Imaging, 2014, 8 (4) : 959-989. doi: 10.3934/ipi.2014.8.959


Valter Pohjola. An inverse problem for the magnetic Schrödinger operator on a half space with partial data. Inverse Problems & Imaging, 2014, 8 (4) : 1169-1189. doi: 10.3934/ipi.2014.8.1169


Li Liang. Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data. Inverse Problems & Imaging, 2015, 9 (2) : 469-478. doi: 10.3934/ipi.2015.9.469


Soumen Senapati, Manmohan Vashisth. Stability estimate for a partial data inverse problem for the convection-diffusion equation. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021060


Mohsen Tadi. A computational method for an inverse problem in a parabolic system. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 205-218. doi: 10.3934/dcdsb.2009.12.205


Saoussen Sokrani. On the global well-posedness of 3-D Boussinesq system with partial viscosity and axisymmetric data. Discrete & Continuous Dynamical Systems, 2019, 39 (4) : 1613-1650. doi: 10.3934/dcds.2019072


Issam S. Strub, Julie Percelay, Olli-Pekka Tossavainen, Alexandre M. Bayen. Comparison of two data assimilation algorithms for shallow water flows. Networks & Heterogeneous Media, 2009, 4 (2) : 409-430. doi: 10.3934/nhm.2009.4.409


Joshua Hudson, Michael Jolly. Numerical efficacy study of data assimilation for the 2D magnetohydrodynamic equations. Journal of Computational Dynamics, 2019, 6 (1) : 131-145. doi: 10.3934/jcd.2019006

2020 Impact Factor: 1.327


  • PDF downloads (37)
  • HTML views (0)
  • Cited by (3)

[Back to Top]