# A Sequence of Integro-Differential Equations Approximating a Viscous Porous Medium Equation

### Karl Oelschläger

Universität Heidelberg, Germany

## Abstract

We consider a sequence of particular integro-differential equations, whose solutions $ρ_{N}$ converge as $N→∞$ to the solution $ρ$ of a viscous porous medium equation. First, it is demonstrated that under suitable regularity conditions the functions $ρ_{N}$ are smooth uniformly in $N∈N$. Furthermore, an asymptotic expansion for $ρ_{N}$ as \( N \rightarrow \inftly \) is provided, which precisely describes the convergence to $ρ$. The results of this paper are needed in particular for the numerical simulation of a viscous porous medium equation by a particle method.

## Cite this article

Karl Oelschläger, A Sequence of Integro-Differential Equations Approximating a Viscous Porous Medium Equation. Z. Anal. Anwend. 20 (2001), no. 1, pp. 55–91

DOI 10.4171/ZAA/1004