We consider a sequence of particular integro-differential equations, whose solutions converge as to the solution of a viscous porous medium equation. First, it is demonstrated that under suitable regularity conditions the functions are smooth uniformly in . Furthermore, an asymptotic expansion for as \( N \rightarrow \inftly \) is provided, which precisely describes the convergence to . The results of this paper are needed in particular for the numerical simulation of a viscous porous medium equation by a particle method.
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Karl Oelschläger, A Sequence of Integro-Differential Equations Approximating a Viscous Porous Medium Equation. Z. Anal. Anwend. 20 (2001), no. 1, pp. 55–91DOI 10.4171/ZAA/1004