| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 86 | |
| Number of page(s) | 24 | |
| DOI | https://doi.org/10.1051/cocv/2024074 | |
| Published online | 08 November 2024 | |
Quantitative uniqueness estimates for stochastic parabolic equations on the whole Euclidean space
1
School of Mathematics and Statistics, Central South University, Changsha 410083, PR China
2
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China
* Corresponding author: xingwuzeng@whu.edu.cn
Received:
3
March
2024
Accepted:
15
September
2024
In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on the whole Euclidean space is established. This paper generalizes the earlier results in [X. Zhang. Differ. Integral Equ. 21 (2008) 81–93] and [Q. Lü and Z. Yin ESAIM Control Optim. Calc. Var. 21 (2015) 378–398] from a bounded domain to an unbounded one. The proof is based on the locally parabolic-type frequency function method. An observability estimate from measurable sets in time for the same equation is also derived.
Mathematics Subject Classification: 60H15 / 93B05
Key words: Stochastic parabolic equation / unique continuation / unbounded domain
© The authors. Published by EDP Sciences, SMAI 2024
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