Invariant measure of scalar first-order conservation laws with stochastic forcing

• 成果类型: Article
• 署名作者: Debussche, A.; Vovelle, J.
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0599-z
• 发表日期: 2015
• 页码: 575-611
• 关键词: large-time behavior; EQUATIONS

摘要

Under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubic fluxes, we show the existence of an invariant measure. Moreover for sub-quadratic fluxes we show uniqueness and ergodicity of the invariant measure. Also, since this invariant measure is supported by for some small, we are led to generalize to the stochastic case the theory of solutions developed by Chen and Perthame (Ann Inst H Poincar, Anal Non Lin,aire 20(4):645-668, 2003).