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