Free Access
Issue
ESAIM: COCV
Volume 21, Number 2, April-June 2015
Page(s) 378 - 398
DOI https://doi.org/10.1051/cocv/2014027
Published online 09 December 2014
  1. J.P. Dauer, N.I. Mahmudov and M.M. Matar, Approximate controllability of backward stochastic evolution equations in Hilbert spaces. J. Math. Anal. Appl. 323 (2006) 42–56. [CrossRef] [Google Scholar]
  2. L. de Teresa, Approximate controllability of a semilinear heat equation in RN. SIAM J. Control Optim. 36 (1998) 2128–2147. [CrossRef] [MathSciNet] [Google Scholar]
  3. L. Escauriaza, Carleman inequalities and the heat operator. Duke Math. J. 104 (2000) 113–127. [CrossRef] [MathSciNet] [Google Scholar]
  4. L. Escauriaza and L. Vega, Carleman inequalities and the heat operator II. Indiana Univ. Math. J. 50 (2001) 1149–1169. [CrossRef] [MathSciNet] [Google Scholar]
  5. C. Fabre, J.-P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 31–61. [Google Scholar]
  6. E. Fernández-Cara and S. Guerrero, Global Carleman inequalities for parabolic systems and applications to controllability. SIAM J. Control Optim. 45 (2006) 1399–1446. [MathSciNet] [Google Scholar]
  7. E. Fernández-Cara and E. Zuazua, The cost of approximate controllability for heat equations: the linear case. Adv. Differ. Equ. 5 (2000) 465–514. [Google Scholar]
  8. E. Fernández-Cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations. Ann. Inst. Henri Poincaré Anal., Non Linéaire 17 (2000) 583–616. [CrossRef] [MathSciNet] [Google Scholar]
  9. E. Fernández-Cara, M.J. Garrido-Atienza and J. Real, On the approximate controllability of a stochastic parabolic equation with a multiplicative noise. C. R. Acad. Sci. Paris Sér. I Math. 328 (1999) 675–680. [CrossRef] [MathSciNet] [Google Scholar]
  10. A.V. Fursikov and O.Yu. Imanuvilov, Controllability of Evolution Equations. Vol. 34 of Lect. Notes Ser. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul (1996). [Google Scholar]
  11. J.Hadamard, Lectures on Cauchy’s problem in linear partial differential equations. Dover Publications, New York (1953). [Google Scholar]
  12. L. Hörmander, The Analysis of Linear Partial differential operators. III. Pseudodifferential operators. Vol. 274 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (1985). [Google Scholar]
  13. M.M. Lavrentév, V.G. Romanov and S.P. Shishat-skii, Ill-posed Problems of Mathematical Physics and Analysis, Translated from the Russian by J.R. Schulenberger. Vol. 64 of Trans. Math. Monogr. AMS, Providence, RI (1986). [Google Scholar]
  14. G. Lebeau and L. Robbiano, Contrôle exact de l’équation de la chaleur. Commun. Partial Differ. Equ. 20 (1995) 335–356. [Google Scholar]
  15. H. Li and Q. Lü, A quantitative boundary unique continuation for stochastic parabolic equations. J. Math. Anal. Appl. 402 (2013) 518–526. [CrossRef] [Google Scholar]
  16. F. Lin, A uniqueness theorem for parabolic equations. Commun. Pure Appl. Math. 43 (1990) 127–136. [CrossRef] [Google Scholar]
  17. Q. Lü, 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. Lü, Carleman estimate for stochastic parabolic equations and inverse stochastic parabolic problems. Inverse Probl. 28 (2012) 045008. [CrossRef] [MathSciNet] [Google Scholar]
  19. N.I. Mahmudov, Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces. SIAM J. Control Optim. 42 (2003) 1604–1622. [CrossRef] [MathSciNet] [Google Scholar]
  20. K.-D. Phung and G. Wang, Quantitative unique continuation for the semilinear heat equation in a convex domain. J. Funct. Anal. 259 (2010) 1230–1247. [CrossRef] [MathSciNet] [Google Scholar]
  21. K.-D. Phung and G. Wang, An observability estimate for parabolic equations from a measurable set in time and its applications. J. Eur. Math. Soc. 15 (2013) 681–703. [CrossRef] [MathSciNet] [Google Scholar]
  22. K.-D. Phung, L. Wang and C. Zhang, Bang-bang property for time optimal control of semilinear heat equation, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 31 (2014) 477–499. [Google Scholar]
  23. C. Poon, Unique continuation for parabolic equations. Commun. Partial Differ. Equ. 21 (1996) 521–539. [CrossRef] [Google Scholar]
  24. J. Real, Some results on controllability for stochastic heat and Stokes equations. C. R. Acad. Sci. Paris Sér. I Math. 322 (1996) 1197–1202. [Google Scholar]
  25. S. Tang and X. Zhang, Null controllability for forward and backward stochastic parabolic equations. SIAM J. Control Optim. 48 (2009) 2191–2216. [CrossRef] [MathSciNet] [Google Scholar]
  26. S. Vessella, Carleman estimates, optimal three cylinder inequality, and unique continuation properties for solutions to parabolic equations. Commun. Partial Differ. Equ. 28 (2003) 637–676. [CrossRef] [Google Scholar]
  27. M. Yamamoto, Carleman estimates for parabolic equations and applications. Inverse Probl. 25 (2009) 123013. [CrossRef] [Google Scholar]
  28. X. Zhang, Unique continuation for stochastic parabolic equations. Differ. Integral Equ. 21 (2008) 81–93. [Google Scholar]
  29. X. Zhou, A duality analysis on stochastic partial differential equations. J. Funct. Anal. 103 (1992) 275–293. [CrossRef] [MathSciNet] [Google Scholar]
  30. E. Zuazua, Controllability and observability of partial differential equations: some results and open problems. Vol. III of Handbook of differential equations: evolutionary equations. Elsevier/North-Holland, Amsterdam (2007). [Google Scholar]
  31. C. Zuily, Uniqueness and nonuniqueness in the Cauchy Problem. Birkhäuser Boston, Inc., Boston, MA (1983). [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.