Comptes Rendus
Optimal Control/Partial Differential Equations
Carleman inequality for backward stochastic parabolic equations with general coefficients
Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 775-780.

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.09.036

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},
}
TY  - JOUR
AU  - Shanjian Tang
AU  - Xu Zhang
TI  - Carleman inequality for backward stochastic parabolic equations with general coefficients
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 775
EP  - 780
VL  - 339
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crma.2004.09.036
LA  - en
ID  - CRMATH_2004__339_11_775_0
ER  - 
%0 Journal Article
%A Shanjian Tang
%A Xu Zhang
%T Carleman inequality for backward stochastic parabolic equations with general coefficients
%J Comptes Rendus. Mathématique
%D 2004
%P 775-780
%V 339
%N 11
%I Elsevier
%R 10.1016/j.crma.2004.09.036
%G en
%F CRMATH_2004__339_11_775_0
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/

[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

Cited by Sources:

Comments - Policy