Large time solution of an inhomogeneous nonlinear diffusion equation
R. E. Grundy · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1983
Abstract The paper considers the large time solution of the nonlinear diffusion equation ρ(x) ∂u / ∂t = ∂ / ∂x {C(x) uβ ∂u / ∂x}, 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 x∈(-∞, ∞) 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.