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Stability results for weak solutions to backward one-dimensional semi-linear parabolic equations with locally Lipschitz source

  • Dinh Nho Hào ORCID logo EMAIL logo , Nguyen Van Duc ORCID logo and Nguyen Thi Ngoc Oanh ORCID logo

Abstract

Stability estimates of Hölder type for weak solutions to backward one-dimensional semi-linear parabolic equations with locally Lipschitz source are obtained. It is noticed that stability results for weak solutions to nonlinear inverse problems are very rare in the literature.

MSC 2010: 65M32; 65M12; 35R11

Award Identifier / Grant number: B2019-TNA-01.T

Funding statement: This research is supported by Vietnam Institute for Advanced Study in Mathematics (VIASM) and by Vietnam Ministry of Education and Training under grant number B2019-TNA-01.T.

Acknowledgements

The authors thank the reviewers for their constructive comments and suggestions.

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Received: 2020-09-07
Revised: 2021-04-29
Accepted: 2021-06-02
Published Online: 2021-07-01
Published in Print: 2021-08-01

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