On a Nonlinear Degenerate Parabolic Equation in Infiltration or Evaporation through a Porous Medium.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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During the last two decades a great deal of progress has been made on the mathematical analysis of flows through porous media. Such phenomena led to degenerate nonlinear parabolic equations. The equations obtained are of different nature when the fluid movement takes place in a horizontal column of the medium rather than in a vertical column of the medium. The latter case gives rise to first order nonlinear perturbations of the former case and equations of this more general sort also model the evaporation of a fluid through a porous medium. A significant technical difficulty arises in the evaporation case the first order nonlinear terms can be singular at the points where the solution vanishes. In this paper the authors give a mathematical treatment of the Cauchy problem as well as the first and mixed boundary value problems for the relevant equations. Existence, continuity and uniqueness of generalized solutions are proved thereby improving earlier results in the mathematical literature.
- Statistics and Probability
- Fluid Mechanics