Duke Applied Mathematics

Publications [#244257] of Thomas P. Witelski

Papers Published

1. Witelski, TP, Intermediate asymptotics for Richards' equation in a finite layer, Journal of Engineering Mathematics, vol. 45 no. 3-4 (April, 2003), pp. 379-399 [A:1022609020200], [doi]
   (last updated on 2026/01/19)

   Abstract:
   Perturbation methods are applied to study an initial-boundary-value problem for Richards' equation, describing vertical infiltration of water into a finite layer of soil. This problem for the degenerate diffusion equation with convection and Dirichlet/Robin boundary conditions exhibits several different regimes of behavior. Boundary-layer analysis and short-time asymptotics are used to describe the structure of similarity solutions, traveling waves, and other solution states and the transitions connecting these different intermediate asymptotic regimes.