Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 90
Number of page(s) 31
DOI https://doi.org/10.1051/cocv/2024082
Published online 10 December 2024
  1. S.E. Chorfi, G. Guermai, L. Maniar and W. Zouhair, Logarithmic convexity and impulsive controllability for the one-dimensional heat equation with dynamic boundary conditions. IMA J. Math. Control Inform. 29 (2022) 861–891. [CrossRef] [MathSciNet] [Google Scholar]
  2. E. Fernandez-Cara, M. Gonzalez-Burgos, S. Guerrero and J. Puel, Null controllability of the heat equation with boundary Fourier conditions: the linear case. ESAIM: Control Optim. Calc. Var. 12 (2006) 442–465. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  3. E. Fernandez-Cara and S. Guerrero, Global Carleman inequalities for parabolic systems and applications to controllability. SIAM J. Control Optim. 45 (2006) 1395–1446. [CrossRef] [Google Scholar]
  4. A.V. Fursikov and O. Yu. Imanuvilov, Controllability of evolution equations, in Lecture Notes Series, vol. 34 Seoul National University, Seoul, Korea (1996). [Google Scholar]
  5. O. Yu Imanuvilov and M. Yamamoto, Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations. Puhl. Res. Inst. Math. Sci. 39 (2003) 227–274. [CrossRef] [Google Scholar]
  6. G. Lebeau and L. Robbiano, Contrôle exact de l’equation de la chaleur. Commun. Part. Differ. Equ. 20 (1995) 335–356. [CrossRef] [Google Scholar]
  7. J.-L. Lions, Some Aspects of the Optimal Control of Distributed Parameter Systems. SIAM (1972). [CrossRef] [Google Scholar]
  8. L. Maniar, M. Meyries and R. Schnaubelt, Null controllability for parabolic equations with dynamic boundary conditions. Evol. Equ. Control Theory 6 (2017) 381–407. [CrossRef] [MathSciNet] [Google Scholar]
  9. R.A. Morales Ponce, Contribution to inverse problems and controllability issues of hyperbolic and parabolic partial differential equations. PhD thesis, Universidad de Chile (2019). [Google Scholar]
  10. E. Zuazua, Controllability and observability of partial differential equations: some results and open problems, in Handbook of Differential Equations. Elsevier Science Evol. Differ. Equ. 3 (2007) 527–621. [Google Scholar]
  11. V. Barbu, A. Rascanu and G. Tessitore, Carleman estimates and controllability of linear stochastic heat equations. Appl. Math. Optim. 47 (2003) 97–120. [CrossRef] [MathSciNet] [Google Scholar]
  12. M. Baroun, S. Boulite, A. Elgrou and L. Maniar, Null controllability for stochastic parabolic equations with dynamic boundary conditions. J. Dyn. Control Syst. 29 (2023) 1727–1756. [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Chen, Null controllability with constraints on the state for the stochastic heat equation. J. Dyn. Control Syst. 24 (2018) 39–50. [CrossRef] [MathSciNet] [Google Scholar]
  14. X. Liu, Global Carleman estimate for stochastic parabolic equations, and its application. ESAIM: Control Optim. Calc. Var. 20 (2014) 823–839. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  15. X. Liu and Y. Yu, Carleman estimates of some stochastic degenerate parabolic equations and application. SIAM J. Control Optim. 57 (2019) 3527–3552. [CrossRef] [MathSciNet] [Google Scholar]
  16. Q. Lu, Exact controllability for stochastic transport equations. SIAM J. Control Optim. 52 (2014) 397–419. [CrossRef] [MathSciNet] [Google Scholar]
  17. 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]
  18. Q. Lu and Y. Zhongqi, Unique continuation for stochastic heat equations. ESAIM: Control Optim. Calc. Var. 21 (2015) 378–398. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  19. S. Tang and X. Zhang, Null controllability for forward and backward stochastic parabolic equations. SIAM J. Control Optim. 48 (2009) 2191–2216. [Google Scholar]
  20. X. Zhang, Unique continuation for stochastic parabolic equations. Differ. Integral Equ. 21 (2008) 81–93. [Google Scholar]
  21. Q. Lu and X. Zhang, Mathematical Control Theory for Stochastic Partial Differential Equations. Springer (2021). [CrossRef] [Google Scholar]
  22. T. Carleman, Sur un probleme d’unicite pour les systemes d’equations aux derivees partielles a deux variables independantes. Ark. Mat. Astr. Fys. 17 (1939) 1–9. [Google Scholar]
  23. Y. Yan, Carleman estimates for stochastic parabolic equations with Neumann boundary conditions and applications. J. Math. Anal. Applic. 457 (2018) 248–272. [CrossRef] [Google Scholar]
  24. G. Coclite, A. Favini, C. Gal, G. Goldstein, J. Goldstein, E. Obrecht and S. Romanelli, The role of Wentzell boundary conditions in linear and nonlinear analysis. Tübinger Berichte 3 (2009) 279–292. [Google Scholar]
  25. C. Gal, The role of surface diffusion in dynamic boundary conditions: where do we stand? Milan J. Math. 83 (2015) 237–278. [CrossRef] [MathSciNet] [Google Scholar]
  26. G. Goldstein, Derivation and physical interpretation of general boundary conditions. Adv. Differ. Equ. 11 (2006) 457–480. [Google Scholar]
  27. M. Baroun, S. Boulite, A. Elgrou and L. Maniar, Null controllability for backward stochastic parabolic convection- diffusion equations with dynamic boundary conditions. Math. Control Related Fields (2024). [Google Scholar]
  28. I. Chueshov and B. Schmalfuss, Parabolic stochastic partial differential equations with dynamical boundary conditions. Differ. Integral Equ. 17 (2004) 751–780. [Google Scholar]
  29. P. Muller, Stochastic forcing of oceanic motions, in Stochastic Models in Geosystems, vol. 85. Springer New York, New York, NY (1997) 219–237. [CrossRef] [Google Scholar]
  30. D. Yang and J. Duan, An impact of stochastic dynamic boundary conditions on the evolution of the Cahn-Hilliard system. Stochast. Anal. Applic. 25 (2007) 613–639. [CrossRef] [Google Scholar]
  31. 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]
  32. L. Yan and B. Wu, Null controllability for a class of stochastic singular parabolic equations with the convection term, Discrete Continuous Dyn. Syst. B 27 (2022) 3213–3240. [CrossRef] [MathSciNet] [Google Scholar]
  33. Y. Yongyi and Q. Zhao, Controllability and observability for some forward stochastic complex degenerate/singular Ginzburg Landau equations. ESAIM: Control Optim. Calc. Var. 29 (2023) 34. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  34. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Cambridge University Press (2014). [CrossRef] [Google Scholar]
  35. E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation. Syst. Control Lett. 14 (1990) 55–61. [Google Scholar]
  36. E.M. Ouhabaz, Analysis of Heat Equations on Domains. LMS Monograph Series 31., Princeton University Press (2004). [Google Scholar]
  37. A. Lunardi, Interpolation Theory, 2nd edn. Edizioni della Normale, Pisa (2009). [Google Scholar]
  38. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, J. A. Barth, Heidelberg (1995). [Google Scholar]
  39. J.-M. Coron, Control and Nonlinearity. American Mathematical Society (2007). [Google Scholar]

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