Accession Number : ADA116204

Title :   Solutions of the Porous Medium Equation in R(N) under Optimal Conditions on Initial Values.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Benilan,Philippe ; Crandall,Michael G ; Pierre,Michel

PDF Url : ADA116204

Report Date : May 1982

Pagination or Media Count : 49

Abstract : This work establishes existence of solutions of the initial-value problem u(t) = delta (determinant u to m-1 power), u(x,0), = u(0)(x), where m 1, under the most general conditions on u(0). Namely, u(0) need only be such that R to the minus (2 divided by m-1 +N) sum (determinant x or = R) to the power of u(0)(x)) dx is bounded independently of R or = 1. Aronson and Caffarelli have shown this requirement to be necessary. Many auxiliary results are given in the form of estimates on solutions, uniqueness and continuous dependence theorems, etc. While the results may be viewed as 'technical' in that the main points consist of estimates of various sorts, the equation treated is of broad practical interest and the estimates reflect basic properties of the equation. The results obtained are the only ones known to the authors wherein the solvability of a realistic nonlinear initial value problem for a partial differential equation is now understood as completely as in the case of the heat equation.

Descriptors :   *Partial differential equations, *Porous materials, *Boundary value problems, Porosity, Estimates, Theory, Heat

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE