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Stabilization of stationary solutions of evolution equations by noise
A geometric inverse problem for the Boussinesq system
1. | Universidad de Sevilla, Dpto. E.D.A.N., Aptdo. 1160, 41080, Sevilla, Spain |
2. | Dpto., E.D.A.N., Universidad de Sevilla, Aptdo. 1180; 41080 Sevilla |
3. | Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla |
4. | Universidad del Bío-Bío, Dpto. de Ciencias Básicas, Casilla 447, Fernando May, Chillán, Chile |
[1] |
Alexandre J. Chorin, Fei Lu, Robert N. Miller, Matthias Morzfeld, Xuemin Tu. Sampling, feasibility, and priors in data assimilation. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4227-4246. doi: 10.3934/dcds.2016.36.4227 |
[2] |
Dugan Nina, Ademir Fernando Pazoto, Lionel Rosier. Controllability of a 1-D tank containing a fluid modeled by a Boussinesq system. Evolution Equations and Control Theory, 2013, 2 (2) : 379-402. doi: 10.3934/eect.2013.2.379 |
[3] |
Jon Asier Bárcena-Petisco, Kévin Le Balc'h. Local null controllability of the penalized Boussinesq system with a reduced number of controls. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021038 |
[4] |
Yuming Qin, Yang Wang, Xing Su, Jianlin Zhang. Global existence of solutions for the three-dimensional Boussinesq system with anisotropic data. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1563-1581. doi: 10.3934/dcds.2016.36.1563 |
[5] |
Pedro Caro. On an inverse problem in electromagnetism with local data: stability and uniqueness. Inverse Problems and Imaging, 2011, 5 (2) : 297-322. doi: 10.3934/ipi.2011.5.297 |
[6] |
Victor Isakov. On uniqueness in the inverse conductivity problem with local data. Inverse Problems and Imaging, 2007, 1 (1) : 95-105. doi: 10.3934/ipi.2007.1.95 |
[7] |
Débora A. F. Albanez, Maicon J. Benvenutti. Continuous data assimilation algorithm for simplified Bardina model. Evolution Equations and Control Theory, 2018, 7 (1) : 33-52. doi: 10.3934/eect.2018002 |
[8] |
Jochen Bröcker. Existence and uniqueness for variational data assimilation in continuous time. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021050 |
[9] |
Jules Guillot, Emmanuel Frénod, Pierre Ailliot. Physics informed model error for data assimilation. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022059 |
[10] |
Xiaoqiang Dai, Shaohua Chen. Global well-posedness for the Cauchy problem of generalized Boussinesq equations in the control problem regarding initial data. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4201-4211. doi: 10.3934/dcdss.2021114 |
[11] |
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 and Applied Analysis, 2009, 8 (1) : 311-333. doi: 10.3934/cpaa.2009.8.311 |
[12] |
Nicolás Carreño. Local controllability of the $N$-dimensional Boussinesq system with $N-1$ scalar controls in an arbitrary control domain. Mathematical Control and Related Fields, 2012, 2 (4) : 361-382. doi: 10.3934/mcrf.2012.2.361 |
[13] |
Suman Kumar Sahoo, Manmohan Vashisth. A partial data inverse problem for the convection-diffusion equation. Inverse Problems and Imaging, 2020, 14 (1) : 53-75. doi: 10.3934/ipi.2019063 |
[14] |
Francis J. Chung. Partial data for the Neumann-Dirichlet magnetic Schrödinger inverse problem. Inverse Problems and Imaging, 2014, 8 (4) : 959-989. doi: 10.3934/ipi.2014.8.959 |
[15] |
Valter Pohjola. An inverse problem for the magnetic Schrödinger operator on a half space with partial data. Inverse Problems and Imaging, 2014, 8 (4) : 1169-1189. doi: 10.3934/ipi.2014.8.1169 |
[16] |
Li Liang. Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data. Inverse Problems and Imaging, 2015, 9 (2) : 469-478. doi: 10.3934/ipi.2015.9.469 |
[17] |
Soumen Senapati, Manmohan Vashisth. Stability estimate for a partial data inverse problem for the convection-diffusion equation. Evolution Equations and Control Theory, 2021 doi: 10.3934/eect.2021060 |
[18] |
Mohsen Tadi. A computational method for an inverse problem in a parabolic system. Discrete and Continuous Dynamical Systems - B, 2009, 12 (1) : 205-218. doi: 10.3934/dcdsb.2009.12.205 |
[19] |
Saoussen Sokrani. On the global well-posedness of 3-D Boussinesq system with partial viscosity and axisymmetric data. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 1613-1650. doi: 10.3934/dcds.2019072 |
[20] |
Issam S. Strub, Julie Percelay, Olli-Pekka Tossavainen, Alexandre M. Bayen. Comparison of two data assimilation algorithms for shallow water flows. Networks and Heterogeneous Media, 2009, 4 (2) : 409-430. doi: 10.3934/nhm.2009.4.409 |
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