Exponential stability of the flow for a generalized Burgers equation on a circle
- Authors: Djurdjevac A.1, Shirikyan A.R.2,3
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Affiliations:
- Freie Universitat Berlin
- CY Cergy Paris University
- RUDN University
- Issue: Vol 69, No 4 (2023)
- Pages: 588-598
- Section: Articles
- URL: https://journals.rudn.ru/CMFD/article/view/37478
- DOI: https://doi.org/10.22363/2413-3639-2023-69-4-588-598
- EDN: https://elibrary.ru/YFDPHA
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Abstract
The paper deals with the problem of stability for the flow of the 1D Burgers equation on a circle. Using some ideas from the theory of positivity preserving semigroups, we establish the strong contraction in the \(L^1\) norm. As a consequence, it is proved that the equation with a bounded external force possesses a unique bounded solution on \(R\), which is exponentially stable in \(H^1\) as \(t\to+\infty\). In the case of a random external force, we show that the difference between two trajectories goes to zero with probability \(1\).
About the authors
A. Djurdjevac
Freie Universitat Berlin
Author for correspondence.
Email: adjurdjevac@zedat.fu-berlin.de
Berlin, Germany
A. R. Shirikyan
CY Cergy Paris University; RUDN University
Email: Armen.Shirikyan@cyu.fr
Cergy-Pontoise, France; Moscow, Russia
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