Observability inequalities for the backward stochastic evolution equations and their applications

2023/08/22 by Liu, Yuanhang, Wu, Weijia, Yang, Donghui +1 · 1 citation
#93B05 #93B07 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2308.11121

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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• A noncommunicative Kalman condition for null controllability of backward stochastic parabolic systems

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