Exponential stability of the flow for a generalised Burgers equation on a circle
| Autor: | Djurdjevac, Ana, Shirikyan, Armen |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $\mathbb R$, 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 $1$. Comment: 13 pages |
| Databáze: | arXiv |
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