We investigate the asymptotic behaviour of solutions of the convection- diffusion equation $$ b(u)_t + divleft( u q - n u right) = 0 qquad hbox{for r = |x| > e quadhbox{andquad t>0, $$ where $q=l/r, er $, $l>0$. The asymptotic limits that we consider are $ttoinfty$ and $e downto0$. We prove that self-similar solutions of this equation exist, and that are attractors in a class of solutions of the initial-boundary value problem with a flux boundary condition at $r=e$. We give estimates of the rate of convergence in an integral sense and in the $L^infty$-norm.

Degenerate parabolic equations (msc 35K65), Nonlinear initial value problems for linear parabolic equations (msc 35K60), Asymptotic behavior of solutions (msc 35B40)
Department of Analysis, Algebra and Geometry [AM]

van Duijn, C.J, & Peletier, M.A. (1996). Asymptotic behaviour of solutions of a nonlinear transport equation. Department of Analysis, Algebra and Geometry [AM]. CWI.