Compression Effects in Heterogeneous Media

D. Bresch (1) , Š Nečasová (2) , C. Perrin (3)

1 LAMA - Laboratoire de Mathématiques
2 IM / CAS - Institute of Mathematics of the Czech Academy of Science
3 I2M - Institut de Mathématiques de Marseille

We study in this paper compression effects in heterogeneous media with maximal packing constraint. Starting from compressible Brinkman equations, where maximal packing is encoded in a singular pressure and a singular bulk viscosity, we show that the global weak solutions converge (up to a sub-sequence) to global weak solutions of the two-phase compressible/incompressible Brinkman equations with respect to a parameter ε which measures effects close to the maximal packing value. Depending on the importance of the bulk viscosity with respect to the pressure in the dense regimes, memory effects are activated or not at the limit in the congested (incompressible) domain.

Mots clés: Compressible Brinkman Equations; Maximal Packing; Singular Limit; Free Boundary Problem; Memory Effect; Memory Effect MSC: 35Q35; 35B25; 76T20

Domaines: Equations aux dérivées partielles [math.AP]

D. Bresch, Š Nečasová, C. Perrin. Compression Effects in Heterogeneous Media. Journal de l'École polytechnique — Mathématiques, 2019. ⟨hal-01838014v2⟩