Math @ Duke

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. 34
(2003),
pp. 379399 [A:1022609020200], [doi]
(last updated on 2017/12/13)
Abstract: Perturbation methods are applied to study an initialboundaryvalue 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. Boundarylayer analysis and shorttime 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.


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