Journal
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Volume 126, Issue 7, Pages 2163-2179Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.spa.2016.01.007
Keywords
Stochastic parabolic equation; Backward uniqueness; Approximating controllability
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Funding
- CNCS-UEFISCDI project [PN-II-ID-PCE-2012-4-0456]
- Bibos-Research Centre
- Romanian National Authority for Scientific Research
- DFG [CRC 701]
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One proves here the backward uniqueness of solutions to stochastic semilinear parabolic equations and also for the tamed Navier Stokes equations driven by linearly multiplicative Gaussian noises. Applications to approximate controllability of nonlinear stochastic parabolic equations with initial controllers are given. The method of proof relies on the logarithmic convexity property known to hold for solutions to linear evolution equations in Hilbert spaces with self-adjoint principal part. (C) 2016 Elsevier B.V. All rights reserved.
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