Open Access
Issue |
ESAIM: COCV
Volume 28, 2022
|
|
---|---|---|
Article Number | 22 | |
Number of page(s) | 33 | |
DOI | https://doi.org/10.1051/cocv/2022016 | |
Published online | 17 March 2022 |
- F. Abergel and R. Temam, On some control problems in fluid mechanics. Theoret. Comput. Fluid Dyn. 1 (1990) 303–325. [Google Scholar]
- R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
- D.N. Arnold, F. Brezzi, and M. Fortin, A stable finite element for the Stokes equations. Calcolo 21 (1984) 337–44. [CrossRef] [MathSciNet] [Google Scholar]
- J.L. Boldrini, E. Fernandéz-Cara and M. A. Rojas-Medar, An optimal control problem for a generalized Boussinesq model: the time dependent case. Rev. Mat. Complete. 20 (2007) 339–366. [Google Scholar]
- E. Casas, C. Clason and K. Kunisch, Approximation of elliptic control problems in measure spaces with sparse solutions. SIAM J. Control Optim. 50 (2012) 1735–52. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas, C. Clason and K. Kunisch, Parabolic control problems in measure spaces with sparse solutions. SIAM J. Control Optim. 51 (2013) 28–63. [Google Scholar]
- E. Casas and K. Kunisch, Optimal control of semilinear elliptic equations in measure spaces. SIAM J. Control Optim. 52 (2014) 339–64. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas and K. Kunisch, Optimal control of the two-dimensional stationary Navier–Stokes equations with measure valued controls. SIAM J. Control Optim. 57 (2019) 1328–54. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas and K. Kunisch, Parabolic control problems in space-time measure spaces. ESAIM: COCV 22 (2016) 355–70. [CrossRef] [EDP Sciences] [Google Scholar]
- C. Clason and K. Kunisch, A duality-based approach to elliptic control problems in non-reflexive Banach spaces. ESAIM: COCV 17 (2011) 243–66. [CrossRef] [EDP Sciences] [Google Scholar]
- A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. Springer (2004). [CrossRef] [Google Scholar]
- G. Galdi, An Introduction to the Mathematical Theory of the Navier–Stokes Equations. Springer, New York (2011). [Google Scholar]
- V. Girault and P. A. Raviart, Finite Element Methods for Navier–Stokes Equations: Theory and Algorithms. Springer-Verlag, Berlin (1986). [CrossRef] [Google Scholar]
- M. Hinze and U. Matthes, Optimal and model predictive control of the Boussinesq approximation, in Control of Coupled Partial Differential Equations, edited by K. Kunisch, J. Sprekels, G. Leugering and F. Tröltzsch. Birkhäuser Basel (2007). [Google Scholar]
- K. Ito and S.S. Ravindran, Optimal control of thermally convected fluid flows. SIAM J. Sci. Comput. 19 (1998) 1847–1869. [CrossRef] [MathSciNet] [Google Scholar]
- H. Kim, Existence and regularity of very weak solutions of the stationary Navier–Stokes equations. Arch. Ration. Mech. Anal. 193 (2009) 117–52. [CrossRef] [MathSciNet] [Google Scholar]
- H. Kim, The existence and uniqueness of very weak solutions of the stationary Boussinesq system. Nonlinear Anal. Real World Appl. 75 (2012) 317–30. [CrossRef] [Google Scholar]
- K. Kunisch, K. Pieper and B. Vexler, Measure valued directional sparsity for parabolic optimal control problems. SIAM J. Control Optim. 52 (2014) 3078–3108. [Google Scholar]
- K. Kunisch, P. Trautmann and B. Vexler, Optimal control of the undamped linear wave equation with measure valued controls. SIAM J. Control Optim. 54 (2016) 1212–44. [CrossRef] [MathSciNet] [Google Scholar]
- B. Kummer, Newton’s method based on generalized derivatives for nonsmooth functions: Convergence analysis, edited by Oettli W., Pallaschke D. Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 382. Springer, Berlin, Heidelberg (1992) 171–94. [CrossRef] [Google Scholar]
- H.-C. Lee and B. C. Shin, Piecewise optimal distributed controls for 2D Boussinesq equations. Math. Methods Appl. Sci. 23 (2000) 227–54. [CrossRef] [MathSciNet] [Google Scholar]
- H.-C. Lee and O.Yu. Imanuvilov, Analysis of optimal control problems for the 2-D stationary Boussinesq equations. J. Math. Anal. Appl. 242 (2000) 191–211. [CrossRef] [MathSciNet] [Google Scholar]
- J. M. Mihaljan, A rigorous exposition of the Boussinesq approximations applicable to a thin layer of fluid. Astrophys. J. 136 (1962) 1126–33. [CrossRef] [MathSciNet] [Google Scholar]
- L. Qi and J. Sun, A nonsmooth version of Newton’s method. Math. Program. 58 (1993) 353–67. [CrossRef] [Google Scholar]
- W. Rudin, Real and Complex Analysis. McGraw-Hill Book Co., London (1970). [Google Scholar]
- P.A. Tapia, Lp-theory for the Boussinesq system, Ph.D. thesis, University of Chile (2015). [Google Scholar]
- F. Tröltzsch and D. Wachsmuth, Second-order sufficient optimality conditions for the optimal control of Navier–Stokes equations. ESAIM: COCV 12 (2006) 353–67. [Google Scholar]
- E. Zeidler, Nonlinear Functional Analysis and its Applications I, Springer-Verlag, New York (1986). [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.