Large Time Solution of an Inhomogeneous Nonlinear Diffusion Equation
Abstract
The paper considers the large time solution of the nonlinear diffusion equation ρ(x)partial u/partial t = partial/partial xbig\{C(x) u^βpartial u/partial x big\}, β > 0, for initial data with compact support. The asymptotic behaviour of ρ(x) and C(x) as x >∞ defines a parameter space, and the nature of the solution at large time depends crucially on the location therein. The paper examines the nature and uniformity of the asymptotic solutions for xin ( ∞,∞) in a restricted region of the entire parameter space, and in certain cases gives the leading error terms. A new integral invariant of the solution is also given.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 April 1983
 DOI:
 10.1098/rspa.1983.0040
 Bibcode:
 1983RSPSA.386..347G