|
|||||
|
|
Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case |
|
| Authors: | Viorel Barbu Michael R?ckner Francesco Russo |
| Institution: | 1. University A1.I. Cuza, 6600, Iasi, Romania 2. Fakult?t f??r Mathematik, Universit?t Bielefeld, 33615, Bielefeld, Germany 3. Department of Mathematics and Statistics, Purdue University, W. Lafayette, IN, 47907, USA 4. INRIA Rocquencourt, Equipe MathFi and Cermics Ecole des Ponts, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153, Le Chesnay Cedex, France 5. Ecole Nationale Sup??rieure des Techniques Avanc??es (ENSTA, ParisTech), Paris, France |
| Abstract: | We consider a possibly degenerate porous media type equation over all of ${\mathbb R^d}$ 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. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |