Djurdjevac, Ana and Shirikyan, A. R. (2024) Exponential Stability of the Flow for a Generalized Burgers Equation on a Circle. Journal of Mathematical Sciences, 285 .
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Official URL: https://doi.org/10.1007/s10958-024-07474-6
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 L1 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 H1 as t → +∞. In the case of a random external force, we show that the difference between two trajectories goes to zero with probability 1.
| Item Type: | Article |
|---|---|
| Subjects: | Mathematical and Computer Sciences Mathematical and Computer Sciences > Mathematics Mathematical and Computer Sciences > Mathematics > Applied Mathematics |
| Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |
| ID Code: | 3291 |
| Deposited By: | Lukas-Maximilian Jaeger |
| Deposited On: | 29 Oct 2025 12:58 |
| Last Modified: | 29 Oct 2025 12:58 |
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