In this paper, we solve a local state observation problem for stochastic hyperbolic equations without boundary conditions, which is reduced to a local unique continuation property for these equations. This result is proved by a global Carleman estimate. As far as we know, this is the first result in this topic.
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DOI : 10.1051/cocv/2019049
Keywords: Stochastic hyperbolic equation, Carleman estimate, local state observation, local unique continuation
@article{COCV_2020__26_1_A79_0,
author = {L\"u, Qi and Yin, Zhongqi},
title = {Local state observation for stochastic hyperbolic equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2020},
publisher = {EDP Sciences},
volume = {26},
doi = {10.1051/cocv/2019049},
mrnumber = {4156827},
zbl = {1460.93018},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2019049/}
}
TY - JOUR AU - Lü, Qi AU - Yin, Zhongqi TI - Local state observation for stochastic hyperbolic equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2019049/ DO - 10.1051/cocv/2019049 LA - en ID - COCV_2020__26_1_A79_0 ER -
%0 Journal Article %A Lü, Qi %A Yin, Zhongqi %T Local state observation for stochastic hyperbolic equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2019049/ %R 10.1051/cocv/2019049 %G en %F COCV_2020__26_1_A79_0
Lü, Qi; Yin, Zhongqi. Local state observation for stochastic hyperbolic equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 79. doi: 10.1051/cocv/2019049
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Cité par Sources :
This work is partially supported by NSF of China under grants 11971334 and 11931011, and the General Fund Project of Sichuan Provincial Department of Education in China under grant 13ZB0164.
