Carleman and Observability Estimates for Stochastic Wave Equations

Xu Zhang

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Carleman and Observability Estimates for Stochastic Wave Equations

Xu Zhang

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Abstract

Based on a fundamental identity for stochastic hyperbolic-like operators, we derive in this paper a global Carleman estimate (with singular weight function) for stochastic wave equations. This leads to an observability estimate for stochastic wave equations with non-smooth lower order terms. Moreover, the observability constant is estimated by an explicit function of the norm of the involved coefficients in the equation.

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Xu Zhang. 2007-03-20. Carleman and Observability Estimates for Stochastic Wave Equations. https://arxiv.org/abs/math/0703599

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