A weighted identity for stochastic partial differential operators and its applications
Optimization and Control
2015-08-21 v1 Analysis of PDEs
Abstract
In this paper, a pointwise weighted identity for some stochastic partial differential operators (with complex principal parts) is established. This identity presents a unified approach in studying the controllability, observability and inverse problems for some deterministic/stochastic partial differential equations. Based on this identity, one can deduce all the known Carleman estimates and observability results, for some deterministic partial differential equations, stochastic heat equations, stochastic Schr\"odinger equations and stochastic transport equations. Meanwhile, as its new application, we study an inverse problem for linear stochastic complex Ginzburg-Landau equations.
Cite
@article{arxiv.1508.05066,
title = {A weighted identity for stochastic partial differential operators and its applications},
author = {Xiaoyu Fu and Xu Liu},
journal= {arXiv preprint arXiv:1508.05066},
year = {2015}
}