Open Access
| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 98 | |
| Number of page(s) | 28 | |
| DOI | https://doi.org/10.1051/cocv/2025082 | |
| Published online | 05 December 2025 | |
- V. Barbu, Exact controllability of the superlinear heat equation. Appl. Math. Optim. 42 (2000) 73-89. [Google Scholar]
- A. Doubova, E. Fernandez-Cara, M Gonzalez-Burgos and E Zuazua, On the controllability of parabolic systems with a nonlinear term involving the state and the gradient. SIAM J. Control Optim. 41 (2002) 798-819. [Google Scholar]
- E. Fernandez-Cara, Null controllability of the semilinear heat equation. ESAIM Control Optim. Calc. Var. 2 (1997) 87-103. [Google Scholar]
- E. Fernandez-Cara and E Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations. Ann. Inst. H. Poincare C Anal. Non Linéaire 17(2000) 583-616. [Google Scholar]
- A.V. Fursikov and O.Y. Imanuvilov, Controllability of Evolution Equations, Lecture Notes Series, Seoul National University, Research Institute of Mathematics. Global Analysis Research Center, Seoul (1996). [Google Scholar]
- K. Le Balc'h, Global null-controllability and nonnegative-controllability of slightly superlinear heat equations. J. Math. Pures Appl. 135 (2020) 103-139. [Google Scholar]
- Hernandez-Santamaria, K. Le Balc'h and L Peralta, Statistical null-controllability of stochastic nonlinear parabolic equations. Stoch. Partial Differ. Equ. Anal. Comput. 10 (2022) 190-222. [Google Scholar]
- Hernandez-Santamaria, K. Le Balc'h and L Peralta, Global null-controllability for stochastic semilinear parabolic equations. Ann. Inst. H. Poincarée Anal. Non Linéeaire 40 (2023) 1415-1455. [Google Scholar]
- L. Zhang, F. Xu and B. Liu, New global Carleman estimates and null controllability for forward/backward semi-linear parabolic SPDEs (2024), arXiv:2401.13455. [Google Scholar]
- S. Zhang, H. Gao and G. Yuan, New global Carleman estimates and null controllability for a stochastic Cahn-Hilliard type equation. J. Differ. Equ. 430(2025) 113203. [Google Scholar]
- Q. Lu and X. Zhang, Mathematical Control Theory for Stochastic Partial Differential Equations, Probability Theory and Stochastic Modelling. Springer Nature Switzerland AG (2021). [Google Scholar]
- Q. Lu, Some results on the controllability of forward stochastic heat equations with control on the drift. J. Funct. Anal. 260 (2011) 832-851. [CrossRef] [MathSciNet] [Google Scholar]
- D. Yang and J. Zhong, Observability inequality of backward stochastic heat equations for measurable sets and its applications. SIAM J. Control Optim. 54 (2016) 1157-1175. [CrossRef] [MathSciNet] [Google Scholar]
- K. Beauchard and F. Marbach, Unexpected quadratic behaviors for the small-time local null controllability of scalar-input parabolic equations. J. Math. Pures Appl. 136 (2020) 22-91. [Google Scholar]
- F. Boyer and J. Le Rousseau, Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations. Ann. Inst. Henri Poincare, Anal. Non Linéaire 31 (2014) 1035-1078. [Google Scholar]
- D. Allonsius, F. Boyer and M. Morancey, Spectral analysis of discrete elliptic operators and applications in control theory. Numer. Math. 140(2018) 857-911. [Google Scholar]
- F. Boyer, F. Hubert and J. Le Rousseau, Discrete Carleman estimates for elliptic operators and uniform controllability of semi-discretized parabolic equations. J. Math. Pures Appl. 93 (2010) 240-276. [Google Scholar]
- E. Cerpa, R. Lecaros, T.N.T. Nguyen and A. Pérez, Carleman estimates and controllability for a semi-discrete fourth-order parabolic equation. J. Math. Pures Appl. 164 (2022) 93-130. [Google Scholar]
- S. Labbe and E. Trelat, Uniform controllability of semidiscrete approximations of parabolic control systems. Syst. Control Lett. 55 (2006) 597-609. [CrossRef] [Google Scholar]
- T.N.T. Nguyen, Uniform controllability of semidiscrete approximations for parabolic systems in Banach spaces. Discrete Contin. Dyn. Syst. Ser. B 20 (2015) 613-640. [Google Scholar]
- E. Zuazua, Propagation, observation, and control of waves approximated by finite difference methods. SIAM Rev. 47(2005) 197-243. [CrossRef] [MathSciNet] [Google Scholar]
- E. Zuazua, Control and numerical approximation of the wave and heat equations, in International Congress of Mathematicians, Vol. III. Eur. Math. Soc., Zu rich (2006) 1389-1417. [Google Scholar]
- Q. Zhao, Null controllability for stochastic semi-discrete parabolic equations, SIAM J. Control Optim. 63 (2025) 2007-2028. [Google Scholar]
- Y. Wang and Q. Zhao, Null controllability for stochastic fourth order semi-discrete parabolic equations (2024), arXiv:2405.03257. [Google Scholar]
- F. Boyer, On the penalised HUM approach and its applications to the numerical approximation of null-controls for parabolic problems, in CANUM 2012, 41e Congres National d'Analyse Numérique, in: ESAIM Proc., 41, EDP Sciences, Les Ulis (2013) 15-58. [Google Scholar]
- F. Boyer, F. Hubert and J. Le Rousseau, Discrete Carleman estimates for elliptic operators in arbitrary dimension and applications. SIAM J. Control Optim. 48 (2010) 5357-5397. [CrossRef] [MathSciNet] [Google Scholar]
- R. Lecaros, J.H. Ortega and A. Perez, Stability estimate for the semi-discrete linearized benjamin-bona-mahony equation. ESAIM: Control Optim. Calc. Var. 27(2021) 93. [Google Scholar]
- J.-L. Lions, Optimal control of systems governed by partial differential equations, in Die Grundlehren der mathematischen Wissenschaften, Band 170. Springer-Verlag, New York-Berlin (1971). Translated from the French by S. K. Mitter. [Google Scholar]
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