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20-11-2019 | Focus

The stability analysis for uncertain heat equations based on p-th moment

Authors: Jin Liu, Yi Zhang

Published in: Soft Computing | Issue 4/2020

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Abstract

Stability in p-th moment plays a vital role in uncertain heat equation (UHE). However, little is known about the definition and properties of stability in p-th moment for UHE. This paper fills this gap and advances the concept of stability in p-th moment for UHE. Based on Markov inequality, this study shows the relationship between stability in p-th moment and stability in measure, that is if an UHE is stable in p-th moment, then it is stable in measure, but not vice versa. Our analysis further reveals that if the coefficients of UHE satisfy strong Lipschitz condition, and meanwhile, the Lipschitz coefficients meet some integral constraints, then the UHE is stable in p-th moment. This study provides a strong theoretically foundation for understanding the stability in p-th moment of UHE.

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Title: The stability analysis for uncertain heat equations based on p-th moment
Authors: Jin Liu
Yi Zhang
Publication date: 20-11-2019
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 4/2020
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-019-04529-8

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