ISSN:
1432-0673
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract From the mathematical formulation of a one-dimensional flow through a partially saturated porous medium, we arrive at a nonlinear free boundary problem, the boundary being between the saturated and the unsaturated regions in the medium. In particular we obtain an equation which is parabolic in the unsaturated part of the domain and elliptic in the saturated part. Existence, uniqueness, a maximum principle and regularity properties are proved for weak solutions of a Cauchy-Dirichlet problem in the cylinder {(x,t): 0≦x≦1, t≧0} and the nature, in particular the regularity, of the free boundary is discussed. Finally, it is shown that solutions of a large class of Cauchy-Dirichlet problems converge towards a stationary solution as t → ∞ and estimates are given for the rate of convergence.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00250838
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