## Differential and Integral Equations

### Classical solutions for a multicomponent flow model in porous media

#### Abstract

We consider an initial-boundary-value problem for a nonlinear differential system consisting of one equation of parabolic type coupled with an $n \times n$ semilinear hyperbolic system of first order. This system of equations describes the compressible, $( n +1 )$-component, miscible displacement in a porous medium, without including effects of molecular diffusion and dispersion. Assuming some regularity conditions on the data, we prove the existence (locally in time) and uniqueness of classical solutions.

#### Article information

Source
Differential Integral Equations Volume 17, Number 7-8 (2004), 893-920.

Dates
First available in Project Euclid: 21 December 2012