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arXiv · 2308.11121

Observability inequalities for the backward stochastic evolution equations and their applications

Yuanhang Liu·Weijia Wu·Donghui Yang·Jie Zhong
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Abstract

The present article delves into the investigation of observability inequalities pertaining to backward stochastic evolution equations. We employ a combination of spectral inequalities, interpolation inequalities, and the telegraph series method as our primary tools to directly establish observability inequalities. Furthermore, we explore three specific equations as application examples: a stochastic degenerate equation, a stochastic fourth order parabolic equation and a stochastic heat equation. It is noteworthy that these equations can be rendered null controllability with only one control in the drift term to each system.

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Yuanhang Liu, Weijia Wu, Donghui Yang, Jie Zhong. 2023-08-22. Observability inequalities for the backward stochastic evolution equations and their applications. https://arxiv.org/abs/2308.11121

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