Eigenvalues of the Barenblatt-Pattle similarity solution in nonlinear diffusion

Source abstract

Abstract We consider the large-time behaviour of the nonlinear diffusion equation ∂u/∂t = r1-μ∂/∂r (rμ-1uβ ∂u/∂r), u ≽ 0, β ≻ 0 for certain types of compact initial data. We show that the solution approaches the Barenblatt-Pattle similarity solution through an infinite sequence of negative real powers of t, which can be found in explicit form. These, together with their interactive product terms, determine the power-series development of u(r,t) as t → ∞.