Carleman and Observability Estimates for Stochastic Wave Equations

2007/03/20 by Zhang, Xu · 1 citation
#35B45 #93B07 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.math/0703599

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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• Lipschitz stability for an inverse problem of a fully-discrete stochastic hyperbolic equation

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