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Stabilization estimates for the Brinkman–Forchheimer–Kelvin–Voigt equation backward in time

Gentile, Maurizio; Straughan, Brian

Stabilization estimates for the Brinkman–Forchheimer–Kelvin–Voigt equation backward in time Thumbnail


Authors

Maurizio Gentile

Brian Straughan



Abstract

The final value value problem for the Brinkman–Forchheimer–Kelvin–Voigt equations is analysed for quadratic and cubic types of Forchheimer nonlinearity. The main term in the Forchheimer equations is allowed to be fully anisotropic. It is shown that the solution depends continuously on the final data provided the solution satisfies an a priori bound in L3.
The technique employed avoids the use of a specialist method for an improperly posed problem such as logarithmic convexity.

Citation

Gentile, M., & Straughan, B. (2023). Stabilization estimates for the Brinkman–Forchheimer–Kelvin–Voigt equation backward in time. Acta Mechanica, 234(9), 4001-4009. https://doi.org/10.1007/s00707-023-03592-5

Journal Article Type Article
Acceptance Date Apr 24, 2023
Online Publication Date May 23, 2023
Publication Date 2023
Deposit Date Oct 20, 2023
Publicly Available Date Oct 20, 2023
Journal Acta Mechanica
Print ISSN 0001-5970
Electronic ISSN 1619-6937
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 234
Issue 9
Pages 4001-4009
DOI https://doi.org/10.1007/s00707-023-03592-5
Public URL https://durham-repository.worktribe.com/output/1807208

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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.




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