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arXiv · 2311.12008

Exponential stability of the flow for a generalised Burgers equation on a circle

Ana Djurdjevac·Armen Shirikyan
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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 $\mathbb R$, 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 $1$.

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Ana Djurdjevac, Armen Shirikyan. 2023-11-20. Exponential stability of the flow for a generalised Burgers equation on a circle. https://arxiv.org/abs/2311.12008

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