PROBABILISTIC REPRESENTATION FOR SOLUTIONS OF AN IRREGULAR POROUS MEDIA TYPE EQUATION

• 成果类型: Article
• 署名作者: Blanchard, Philippe; Roeckner, Michael; Russo, Francesco
• 署名单位: University of Bielefeld; University of Bielefeld; Purdue University System; Purdue University; Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Institut Polytechnique de Paris; ENSTA Paris
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP526
• 发表日期: 2010
• 页码: 1870-1900
• 关键词: uniqueness; ut-delta-phi(u)=0; coefficients; EXISTENCE

摘要

We consider a porous media type equation over all of R-d, d = 1, with monotone discontinuous coefficient with linear growth, and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. The interest in such singular porous media equations is due to the fact that they can model systems exhibiting the phenomenon of self-organized criticality. One of the main analytic ingredients of the proof is a new result on uniqueness of distributional solutions of a linear PDE on R-1 with not necessarily continuous coefficients.