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# Zeitschrift für Analysis und ihre Anwendungen

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**Volume 20, Issue 1, 2001, pp. 55–91**

**DOI: 10.4171/ZAA/1004**

Published online: 2001-03-31

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

Karl Oelschläger^{[1]}(1) Universität Heidelberg, Germany

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.

*Keywords: *Integro-differential equations, porous medium equations, asymptotic expansions

Oelschläger Karl: A Sequence of Integro-Differential Equations Approximating a Viscous Porous Medium Equation. *Z. Anal. Anwend.* 20 (2001), 55-91. doi: 10.4171/ZAA/1004