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Zbl 0861.35058
Lévi, Laurent
Unilateral problems for nonlinear convection-reaction equations. (Problèmes unilatéraux pour des équations non linéaires de convection-réaction.) (French)
[J] Ann. Fac. Sci. Toulouse, VI. Sér., Math. 4, No.3, 593-631 (1995). ISSN 0240-2963

The existence and uniqueness for a scalar conservation law related to Dirichlet's homogeneous boundary condition is established. More precisely for the problem $${\partial u\over\partial t}+\text{Div }f(U,t,x)+g(U,t,x)=0,\quad U\ge 0,\tag1$$ two methods are developed: either a penalization of the equation (1) or an approximation procedure by parabolic problems whose diffusion term tends to zero. The model is a transcription, with some simplifications, of the mass conservation law of a chemical component and of the behaviour law. A motivation for this problem comes from the study of the two-phase creep of two fluids (oils and gases) in a porous medium in order to recover the hydrocarbons.
[M.A.Vivaldi (Roma)]

MSC 2000:: *35L65 Conservation laws
76S05 Flows in porous media
35L85 Unilateral problems; variational inequalities (hyperbolic type)

Keywords: penalization; approximation procedure by parabolic problems; two-phase creep

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