Observability Estimate and State Observation Problems for Stochastic Hyperbolic Equations
Optimization and Control
2015-06-15 v2 Mathematical Physics
math.MP
Abstract
In this paper, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic equations. By these inequalities, we study a state observation problem for stochastic hyperbolic equations. As a consequence, we also establish a unique continuation property for stochastic hyperbolic equations.
Cite
@article{arxiv.1305.0800,
title = {Observability Estimate and State Observation Problems for Stochastic Hyperbolic Equations},
author = {Qi Lu},
journal= {arXiv preprint arXiv:1305.0800},
year = {2015}
}