Ergodicity for the randomly forced Korteweg-de Vries-Burgers equation
Peng Gao
公開日: 2025/9/2
Abstract
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, Foia\c{s}-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.