Accession Number : ADA132839

Title :   A Coordinate Transformation for the Porous Media Equation that Renders the Free-Boundary Stationary.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Gurtin,Morton E ; MacCamy,Richard C ; Socolovsky,Eduardo A

PDF Url : ADA132839

Report Date : Aug 1983

Pagination or Media Count : 25

Abstract : We consider the one-dimensional porous media problem ut = u square xx' u(0, x) = u0(x) for initial data sub uo which vanishes outside a finite interval. Solutions of this problem contain a free boundary separating points (t,x) with u(t,x) 0 from those with u(t,x) = 0. We deduce a coordinate transformation x = X(t,p) which renders this free boundary stationary in time. We describe a simple difference scheme based on this transformation and show that, even with a fairly crude mesh, the free boundary is tracked quite accurately.

Descriptors :   *Transformations(Mathematics), Boundary value problems, Algorithms, Porous materials, Media, Theorems

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE