A quantitative internal unique continuation for stochastic parabolic equations

Zhongqi Yin

doi:10.3934/mcrf.2015.5.165

Article Contents

2015, Volume 5, Issue 1: 165-176. Doi: 10.3934/mcrf.2015.5.165

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A quantitative internal unique continuation for stochastic parabolic equations

Zhongqi Yin^1,

1.
School of Mathematics, Sichuan Normal University, Chengdu, 610068

Received: January 2014

Revised: August 2014

Published: March 2015

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Abstract

This paper is addressed to a quantitative internal unique continuation property for stochastic parabolic equations, i.e., we show that each of their solutions can be determined by the observation on any nonempty open subset of the whole region in which the equations evolve. The proof is based on a global Carleman estimate.

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Mathematics Subject Classification: Primary: 60H15; Secondary: 34A12.

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