JournalszaaVol. 20, No. 1pp. 55–91

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

  • Karl Oelschläger

    Universität Heidelberg, Germany
A Sequence of Integro-Differential Equations Approximating a Viscous Porous Medium Equation cover

Abstract

We consider a sequence of particular integro-differential equations, whose solutions ρN\rho_N converge as NN \rightarrow \infty to the solution ρ\rho of a viscous porous medium equation. First, it is demonstrated that under suitable regularity conditions the functions ρN\rho_N are smooth uniformly in NNN \in \mathbb N. Furthermore, an asymptotic expansion for ρN\rho_N as N\inftlyN \rightarrow \inftly is provided, which precisely describes the convergence to ρ\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