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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.01921 |
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Table of Contents:
- Our goal in this paper is to investigate ergodicity of the randomly forced Korteweg-de Vries-Burgers(KdVB) equation driven by non-additive white noise. Under reasonable conditions, we show that exponential ergodicity for KdVB equation driven by a space-time localised noise and ergodicity for KdVB equation driven by a multiplicative white noise. Our proof is based on some newly developed analytical properties for KdVB equation, such as Carleman estimate, truncated observability inequality, Foiaş-Prodi estimate. Combining these analytical properties with coupling method and asymptotic coupling method, we can investigate the long time behavior of randomly forced KdVB equation.