Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case

• 成果类型: Article
• 署名作者: Barbu, Viorel; Roeckner, Michael; Russo, Francesco
• 署名单位: Alexandru Ioan Cuza University; University of Bielefeld; Purdue University System; Purdue University; Institut Polytechnique de Paris; ENSTA Paris
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0291-x
• 发表日期: 2011
• 页码: 1-43
• 关键词: propagation

摘要

We consider a possibly degenerate porous media type equation over all of R-d with d = 1, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analytical properties of the solution.