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The nonlinear diffusion–convection equation on the semiline with time-dependent flux at the origin

F. Calogero^a, S. De Lillo<sup>b

a</sup> University of Rome "La Sapienza"
^b INFN — National Institute of Nuclear Physics

Abstract: The nonlinear diffusion–convection equation is considered as a pheno-menological model of two-phase flow in a semi-infinite porous medium. For such model the initial/boundary value problem is solved with a general initial datum and a boundary condition at the origin representing a time-dependent flux. The problem is reduced to a linear integral equation of Volterra type in one dependent variable; in some cases of applicative interest this eqution can be solved by quadratures.

Language: English

 English version: Theoretical and Mathematical Physics, 1994, 99:2, 531–537

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