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

  • Jin Liu
  • Yi ZhangEmail author
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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.

Keywords

Uncertain process Uncertain heat equation Stability in p-th moment 

Notes

Compliance with ethical standards

Funding

This paper receives no funding.

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Systems EngineeringNational University of Defense TechnologyChangshaChina
  2. 2.School of Economics and ManagementBeijing University of Chemical TechnologyBeijingChina

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