A Sequence of Integro-Differential Equations Approximating a Viscous Porous Medium Equation
Karl Oelschläger · Zeitschrift für Analysis und ihre Anwendungen · 2001
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 \infty 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.