Calculus of Variations and Geometric Measure Theory

A. Figalli - R. Philipowski

Convergence to the viscous porous medium equation and propagation of chaos

created by figalli on 22 May 2008


Accepted Paper

Inserted: 22 may 2008

Journal: ALEA Lat. Am. J. Probab. Math. Stat.
Year: 2008


We study a sequence of nonlinear stochastic differential equations and show that the distributions of the solutions converge to the solution of the viscous porous medium equation with exponent $m > 1$, generalizing the results of Oelschl\"ager (2001) and Philipowski (2006) which concern the case $m=2$. Furthermore we explain how to apply this result to the study of interacting particle systems.

Keywords: Nonlinear stochastic differential equations, Viscous porous medium equation, Interacting particle systems