Publications [#244257] of Thomas P. Witelski
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- 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 2024/04/24)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.