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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, 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

Funding source: Vietnam Institute for Advanced Study in Mathematics

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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