# 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 $\rho_N$ converge as $N \rightarrow \infty$ to the solution $\rho$ of a viscous porous medium equation. First, it is demonstrated that under suitable regularity conditions the functions $\rho_N$ are smooth uniformly in $N \in \mathbb N$. Furthermore, an asymptotic expansion for $\rho_N$ as $N \rightarrow \inftly$ is provided, which precisely describes the convergence to $\rho$. 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