- Thomas P. Witelski, Intermediate asymptotics for Richards' equation in a finite layer,
Journal of Engineering Mathematics, vol. 45 no. 3-4
pp. 379-399 [A:1022609020200] .
(last updated on 2004/02/12)
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 states.