Ergodicity for the randomly forced Korteweg-de Vries-Burgers equation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911133664804864 |
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| author | Gao, Peng |
| author_facet | Gao, Peng |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodicity for the randomly forced Korteweg-de Vries-Burgers equation Gao, Peng Dynamical Systems Probability 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. |
| title | Ergodicity for the randomly forced Korteweg-de Vries-Burgers equation |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2509.01921 |