Differential and Integral Equations

Classical solutions for a multicomponent flow model in porous media

Youcef Amirat and Abdelhamid Ziani

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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

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

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30] 76S05: Flows in porous media; filtration; seepage


Amirat, Youcef; Ziani, Abdelhamid. Classical solutions for a multicomponent flow model in porous media. Differential Integral Equations 17 (2004), no. 7-8, 893--920. https://projecteuclid.org/euclid.die/1356060335

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