Carleman inequality for backward stochastic parabolic equations with general coefficients

Shanjian Tang; Xu Zhang

doi:10.1016/j.crma.2004.09.036

Optimal Control/Partial Differential Equations

Carleman inequality for backward stochastic parabolic equations with general coefficients

Presented by: Philippe G. Ciarlet

Shanjian Tang ¹; Xu Zhang ^2,³

¹ Department of Mathematics, Fudan University, Shanghai 200433, China
² School of Mathematics, Sichuan University, Chengdu 610064, China
³ Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 775-780.

Abstract
Résumé

In this Note, we present a Carleman inequality for linear backward stochastic parabolic equations (BSPEs) with general coefficients, and its applications in the observability of BSPEs, and in the null controllability of forward stochastic parabolic equations with general coefficients.

Dans cette Note, nous présentons une inégalité de Carleman pour les équations linéaires stochastiques paraboliques rétrogradés avec coefficients généraux, et ses applications à l'observabilité des équations stochastiques paraboliques rétrogradés avec coefficients généraux, et à la contrôlabilité nulle des équations stochastiques paraboliques progressives avec coefficients généraux.

Received: 2004-07-27
Accepted: 2004-09-21
Published online: 2004-11-11

DOI: 10.1016/j.crma.2004.09.036

Author's affiliations:

Shanjian Tang ¹; Xu Zhang ^{2, 3}

¹ Department of Mathematics, Fudan University, Shanghai 200433, China
² School of Mathematics, Sichuan University, Chengdu 610064, China
³ Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain

@article{CRMATH_2004__339_11_775_0,
     author = {Shanjian Tang and Xu Zhang},
     title = {Carleman inequality for backward stochastic parabolic equations with general coefficients},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {775--780},
     publisher = {Elsevier},
     volume = {339},
     number = {11},
     year = {2004},
     doi = {10.1016/j.crma.2004.09.036},
     language = {en},
}

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Shanjian Tang; Xu Zhang. Carleman inequality for backward stochastic parabolic equations with general coefficients. Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 775-780. doi : 10.1016/j.crma.2004.09.036. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.036/

References
Cited by

[1] V. Barbu; A. Răşcanu; G. Tessitore Carleman estimate and controllability of linear stochastic heat equations, Appl. Math. Optim., Volume 47 (2003), pp. 97-120

[2] E. Fernández-Cara; M.J. Garrido-Atienza; J. Real On the approximate controllability of a stochastic parabolic equation with a multiplicative noise, C. R. Acad. Sci. Paris, Ser. I, Volume 328 (1999), pp. 675-680

[3] A.V. Fursikov; O.Yu. Imanuvilov Controllability of Evolution Equations, Lecture Notes Ser., vol. 34, Research Institute of Mathematics, Seoul National University, Seoul, Korea, 1994

[4] S. Tang, X. Zhang, Null controllability for forward and backward stochastic parabolic equations, Preprint

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