Networks and Heterogeneous Media (NHM)

A coupling between a non--linear 1D compressible--incompressible limit and the 1D $p$--system in the non smooth case

Pages: 313 - 330, Volume 11, Issue 2, June 2016      doi:10.3934/nhm.2016.11.313

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Rinaldo M. Colombo - INdAM Unit c/o DII, Università degli Studi di Brescia, Via Branze 38, 25123 Brescia, Italy (email)
Graziano Guerra - Dipartimento di Matematica e Applicazioni Via Roberto Cozzi, 55 - 20125 Milano, Italy (email)

Abstract: We consider two compressible immiscible fluids in one space dimension and in the isentropic approximation. The first fluid is surrounded and in contact with the second one. As the sound speed of the first fluid diverges to infinity, we present the proof of rigorous convergence for the fully non--linear compressible to incompressible limit of the coupled dynamics of the two fluids. A linear example is considered in detail, where fully explicit computations are possible.

Keywords:  Incompressible limit, compressible Euler equations, hyperbolic conservation laws.
Mathematics Subject Classification:  Primary: 35L65, 35Q35; Secondary: 35Q31.

Received: April 2015;      Available Online: March 2016.