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Original Articles

Prolongement Unique Des Solutions

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Pages 573-596 | Published online: 09 Apr 2012

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Ching-Lung Lin & Jenn-Nan Wang. (2022) Quantitative uniqueness estimates for the generalized non-stationary Stokes system. Applicable Analysis 101:10, pages 3591-3611.
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Andreas Karageorghis & Daniel Lesnic. (2020) Identification of obstacles immersed in a stationary Oseen fluid via boundary measurements. Inverse Problems in Science and Engineering 28:7, pages 950-967.
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Andrea Ballerini. (2013) Stable determination of a body immersed in a fluid: the nonlinear stationary case. Applicable Analysis 92:3, pages 460-481.
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Laurent Bourgeois & Jérémi Dardé. (2010) About stability and regularization of ill-posed elliptic Cauchy problems: the case of Lipschitz domains. Applicable Analysis 89:11, pages 1745-1768.
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Victor Isakov, Jenn-Nan Wang & Masahiro Yamamoto. (2007) Uniqueness and Stability of Determining the Residual Stress by One Measurement. Communications in Partial Differential Equations 32:5, pages 833-848.
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Norbert Weck. (2002) UNIQUE CONTINUATION FOR A GENERALIZED STOKES SYSTEM. Communications in Partial Differential Equations 27:3-4, pages 425-436.
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Enrique Fernández-Cara, José D. Martín & José Real. (1999) On the approximate controllability of stochastic stokes systems. Stochastic Analysis and Applications 17:4, pages 563-577.
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Rachid Regbaoui. (1999) Strong unique continuation for stokes equations. Communications in Partial Differential Equations 24:9-10, pages 1891-1902.
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Louis Breton, Cristhian Montoya, Pedro González Casanova & Jesús López Estrada. (2024) Identification of a boundary obstacle in a Stokes fluid with Dirichlet–Navier boundary conditions: External measurements. Journal of Mathematical Analysis and Applications 531:1, pages 127814.
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Juraj Földes & Armen Shirikyan. (2024) Rayleigh–Bénard Convection with Stochastic Forcing Localised Near the Bottom. Journal of Dynamics and Differential Equations.
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Erik Burman, Deepika Garg & Janosch Preuss. (2024) Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation. ESAIM: Mathematical Modelling and Numerical Analysis 58:1, pages 223-245.
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R. Triggiani. 2024. Fluids Under Control. Fluids Under Control 63 155 .
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József J. Kolumbán. (2022) Remote trajectory tracking of a rigid body in an incompressible fluid at low Reynolds number. Comptes Rendus. Mathématique 360:G10, pages 1135-1144.
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Imene Aicha Djebour, Takéo Takahashi & Julie Valein. (2022) Feedback stabilization of parabolic systems with input delay. Mathematical Control & Related Fields 12:2, pages 405.
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Jérôme Le Rousseau, Gilles Lebeau & Luc RobbianoJérôme Le Rousseau, Gilles Lebeau & Luc Robbiano. 2022. Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I. Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I 183 214 .
Genni Fragnelli. (2021) N. Lerner: “Carleman Inequalities”. Jahresbericht der Deutschen Mathematiker-Vereinigung 123:4, pages 285-292.
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Debanjana Mitra, Arnab Roy & Takéo Takahashi. (2021) Approximate controllability and stabilizability of a linearized system for the interaction between a viscoelastic fluid and a rigid body. Mathematics of Control, Signals, and Systems 33:4, pages 637-667.
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Roberto Triggiani & Xiang Wan. (2020) Unique Continuation Properties of Over-Determined Static Boussinesq Problems with Application to Uniform Stabilization of Dynamic Boussinesq Systems. Applied Mathematics & Optimization 84:2, pages 2099-2146.
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Irena Lasiecka, Buddhika Priyasad & Roberto Triggiani. (2021) Maximal L-regularity for an abstract evolution equation with applications to closed-loop boundary feedback control problems. Journal of Differential Equations 294, pages 60-87.
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Irena Lasiecka, Buddhika Priyasad & Roberto Triggiani. (2021) Uniform Stabilization of 3D Navier–Stokes Equations in Low Regularity Besov Spaces with Finite Dimensional, Tangential-Like Boundary, Localized Feedback Controllers. Archive for Rational Mechanics and Analysis 241:3, pages 1575-1654.
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Imene Aicha Djebour. (2021) Local null controllability of a fluid–rigid body interaction problem with Navier slip boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations 27, pages 76.
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Sourav Mitra. (2021) Observability and unique continuation of the adjoint of a linearized simplified compressible fluid-structure model in a 2d channel. ESAIM: Control, Optimisation and Calculus of Variations 27, pages S18.
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Jean-Pierre Raymond. 2021. Encyclopedia of Systems and Control. Encyclopedia of Systems and Control 320 326 .
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Jean-Pierre Raymond. 2020. Encyclopedia of Systems and Control. Encyclopedia of Systems and Control 1 7 .
Andreas Karageorghis & Daniel Lesnic. (2019) The method of fundamental solutions for the Oseen steady‐state viscous flow past obstacles of known or unknown shapes. Numerical Methods for Partial Differential Equations 35:6, pages 2103-2119.
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Jean-Pierre Raymond. (2019) Stabilizability of Infinite-Dimensional Systems by Finite-Dimensional Controls. Computational Methods in Applied Mathematics 19:4, pages 797-811.
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Jean-Pierre Raymond. (2019) Stabilizability of Infinite Dimensional Systems by Finite Dimensional Control. Computational Methods in Applied Mathematics 19:2, pages 267-282.
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Sourav Mitra. (2019) Stabilization of the non-homogeneous Navier–Stokes equations in a 2d channel. ESAIM: Control, Optimisation and Calculus of Variations 25, pages 66.
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Mehdi Badra & Takéo Takahashi. (2019) Boundary stabilization of a fluid-rigid body interaction system. IFAC-PapersOnLine 52:2, pages 64-69.
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Elyes Ahmed & Amel Ben Abda. (2018) The sub-Cauchy–Stokes problem: Solvability issues and Lagrange multiplier methods with artificial boundary conditions. Journal of Computational and Applied Mathematics 338, pages 258-279.
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Ana Leonor Silvestre, Takéo Takahashi & Toshiaki Hishida. (2017) A boundary control problem for the steady self-propelled motion of a rigid body in a Navier–Stokes fluid. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 34:6, pages 1507-1541.
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Debayan Maity & Jean-Pierre Raymond. (2016) Feedback Stabilization of the Incompressible Navier–Stokes Equations Coupled with a Damped Elastic System in Two Dimensions. Journal of Mathematical Fluid Mechanics 19:4, pages 773-805.
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Mehdi Badra & Takéo Takahashi. (2017) Feedback boundary stabilization of 2d fluid-structure interaction systems. Discrete & Continuous Dynamical Systems - A 37:5, pages 2315-2373.
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Güher Çamliyurt & Igor Kukavica. (2016) A local asymptotic expansion for a solution of the Stokes system. Evolution Equations and Control Theory 5:4, pages 647-659.
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O. Glass & T. Horsin. (2016) Lagrangian controllability at low Reynolds number. ESAIM: Control, Optimisation and Calculus of Variations 22:4, pages 1040-1053.
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Mehdi Badra, Fabien Caubet & Jérémi Dardé. (2016) Stability estimates for Navier-Stokes equations and application to inverse problems. Discrete and Continuous Dynamical Systems - Series B 21:8, pages 2379-2407.
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Muriel Boulakia. (2016) Quantification of the unique continuation property for the nonstationary Stokes problem. Mathematical Control and Related Fields 6:1, pages 27-52.
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Habib Ammari, Eunjung Lee, Hyeuknam Kwon, Jin Keun Seo & Eung Je Woo. (2015) Mathematical Modeling of Mechanical Vibration-Assisted Conductivity Imaging. SIAM Journal on Applied Mathematics 75:3, pages 1031-1046.
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Phuong Anh Nguyen & Jean-Pierre Raymond. (2015) Boundary Stabilization of the Navier--Stokes Equations in the Case of Mixed Boundary Conditions. SIAM Journal on Control and Optimization 53:5, pages 3006-3039.
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Hanbing Liu. (2014) Boundary optimal feedback controller for time-periodic Stokes–Oseen flows. Nonlinear Differential Equations and Applications NoDEA 21:5, pages 709-735.
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Mehdi Badra & Takéo Takahashi. (2014) On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems. ESAIM: Control, Optimisation and Calculus of Variations 20:3, pages 924-956.
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Jérémi Dardé & Laurent Bourgeois. (2014) The "exterior approach" to solve the inverse obstacle problem for the Stokes system. Inverse Problems and Imaging 8:1, pages 23-51.
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Sébastien Court. (2014) Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part I: The linearized system.. Evolution Equations & Control Theory 3:1, pages 59-82.
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Muriel Boulakia, Anne-Claire Egloffe & Céline Grandmont. (2013) Stability estimates for the unique continuation property of the Stokes system and for an inverse boundary coefficient problem. Inverse Problems 29:11, pages 115001.
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Mamadou Gueye. (2013) Insensitizing controls for the Navier–Stokes equations. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 30:5, pages 825-844.
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Fabien Caubet & Marc Dambrine. (2013) Stability of critical shapes for the drag minimization problem in Stokes flow. Journal de Mathématiques Pures et Appliquées 100:3, pages 327-346.
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Arnaud Münch & Pablo Pedregal. (2013) A least-squares formulation for the approximation of null controls for the Stokes system. Comptes Rendus. Mathématique 351:13-14, pages 545-550.
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Anne-Claire Egloffe. (2013) Lipschitz stability estimate in the inverse Robin problem for the Stokes system. Comptes Rendus. Mathématique 351:13-14, pages 527-531.
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Mihaela Ignatova & Igor Kukavica. (2012) Strong Unique Continuation for the Navier–Stokes Equation with Non-Analytic Forcing. Journal of Dynamics and Differential Equations 25:1, pages 1-15.
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Muriel Boulakia, Anne-Claire Egloffe & Céline Grandmont. (2013) Stability estimates for a Robin coefficient in the two-dimensional Stokes system. Mathematical Control & Related Fields 3:1, pages 21-49.
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Fabien Caubet. (2013) Instability of an Inverse Problem for the Stationary Navier--Stokes Equations. SIAM Journal on Control and Optimization 51:4, pages 2949-2975.
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Jean-Pierre Raymond. 2013. Encyclopedia of Systems and Control. Encyclopedia of Systems and Control 1 9 .
V. Barbu & I. Lasiecka. (2012) The unique continuation property of eigenfunctions to Stokes–Oseen operator is generic with respect to the coefficients. Nonlinear Analysis: Theory, Methods & Applications 75:12, pages 4384-4397.
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Tu Nguyen & Jenn-Nan Wang. (2011) Quantitative uniqueness estimate for the Maxwell system with Lipschitz anisotropic media. Proceedings of the American Mathematical Society 140:2, pages 595-605.
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J.L. Boldrini, A. Doubova, E. Fernández-Cara & M. González-Burgos. (2012) Some Controllability Results for Linear Viscoelastic Fluids. SIAM Journal on Control and Optimization 50:2, pages 900-924.
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Carlos Conca, Erica L Schwindt & Takéo Takahashi. (2012) On the identifiability of a rigid body moving in a stationary viscous fluid. Inverse Problems 28:1, pages 015005.
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MEHDI BADRA, FABIEN CAUBET & MARC DAMBRINE. (2011) DETECTING AN OBSTACLE IMMERSED IN A FLUID BY SHAPE OPTIMIZATION METHODS. Mathematical Models and Methods in Applied Sciences 21:10, pages 2069-2101.
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Ching-Lung Lin, Gen Nakamura & Jenn-Nan Wang. (2010) Optimal three-ball inequalities and quantitative uniqueness for the Lamé system with Lipschitz coefficients. Duke Mathematical Journal 155:1.
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Laurent Bourgeois. (2010) About stability and regularization of ill-posed elliptic Cauchy problems: the case of C 1,1 domains . ESAIM: Mathematical Modelling and Numerical Analysis 44:4, pages 715-735.
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J.-P. Raymond & M. Vanninathan. (2010) Null controllability in a fluid–solid structure model. Journal of Differential Equations 248:7, pages 1826-1865.
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Masahiro Yamamoto. (2009) Carleman estimates for parabolic equations and applications. Inverse Problems 25:12, pages 123013.
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Roberto Triggiani. (2009) Unique continuation from an arbitrary interior subdomain of the variable-coefficient Oseen equation. Nonlinear Analysis: Theory, Methods & Applications 71:10, pages 4967-4976.
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Oleg Yu Imanuvilov, Jean Pierre Puel & Masahiro Yamamoto. (2009) Carleman estimates for parabolic equations with nonhomogeneous boundary conditions. Chinese Annals of Mathematics, Series B 30:4, pages 333-378.
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Jean-Pierre Puel. (2009) A Nonstandard Approach to a Data Assimilation Problem and Tychonov Regularization Revisited. SIAM Journal on Control and Optimization 48:2, pages 1089-1111.
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Carlos Conca, Patricio Cumsille, Jaime Ortega & Lionel Rosier. (2008) On the detection of a moving obstacle in an ideal fluid by a boundary measurement. Inverse Problems 24:4, pages 045001.
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P. Cannarsa, P. Martinez & J. Vancostenoble. (2008) Carleman Estimates for a Class of Degenerate Parabolic Operators. SIAM Journal on Control and Optimization 47:1, pages 1-19.
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Muriel Boulakia & Axel Osses. (2007) Local null controllability of a two-dimensional fluid-structure interaction problem. ESAIM: Control, Optimisation and Calculus of Variations 14:1, pages 1-42.
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Laurent Bourgeois. (2007) A stability estimate for ill-posed elliptic Cauchy problems in a domain with corners. Comptes Rendus. Mathématique 345:7, pages 385-390.
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Oleg Imanuvilov & Takéo Takahashi. (2007) Exact controllability of a fluid–rigid body system. Journal de Mathématiques Pures et Appliquées 87:4, pages 408-437.
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A. DOUBOVA, E. FERNÁNDEZ-CARA & J. H. ORTEGA. (2007) On the identification of a single body immersed in a Navier-Stokes fluid. European Journal of Applied Mathematics 18:1, pages 57-80.
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Anna Doubova, Enrique Fernández-Cara, Manuel González-Burgos & Jaime Ortega. (2006) Uniqueness and partial identification in a geometric inverse problem for the Boussinesq system. Comptes Rendus. Mathématique 342:9, pages 665-670.
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Tu Jin Kim & Qianshun Chang. (2005) REMARK ON UNIQUE CONTINUATION OF SOLUTIONS TO THE STOKES AND THE NAVIER-STOKES EQUATIONS. Acta Mathematica Scientia 25:4, pages 594-598.
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