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Global existence of weak solutions for a parabolic-hyperbolic system arising on dynamics of porous media. (Existence globale de solutions faibles pour un système parabolique-hyperbolique intervenant en dynamique des milieux poreux.) (French. Abridged English version) Zbl 0838.76086
Summary: We deal with an existence result for global weak solutions to a nonlinear parabolic-hyperbolic system coming from compressible miscible displacement processes in porous media. We regularize the hyperbolic equation by adding an artificial diffusion and apply the Schauder fixed point theorem. The uniform estimates and the compensated compactness method are used to prove the existence result.

76S05 Flows in porous media; filtration; seepage
35Q35 PDEs in connection with fluid mechanics