Unilateral problems for nonlinear convection-reaction equations
The existence and uniqueness for a scalar conservation law related to Dirichlet's homogeneous boundary condition is established. More precisely for the problem \[ {\partial u\over\partial t}+\text{Div }f(U,t,x)+g(U,t,x)=0,\quad U\geq 0,\tag{1} \] 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.
approximation procedure by parabolic problems
scientific article; zbMATH DE number 942770
scientific article