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

Rinaldo M.  Colombo; Graziano  Guerra; Rinaldo M.  Colombo; Graziano  Guerra

doi:10.3934/nhm.2016.11.313

Networks and Heterogeneous Media

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

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

Rinaldo M. Colombo ^{1
,},
Graziano Guerra ^{2
,}

1.
INdAM Unit c/o DII, Università degli Studi di Brescia, Via Branze 38, 25123 Brescia
2.
Dipartimento di Matematica e Applicazioni Via Roberto Cozzi, 55 - 20125 Milano

Received: 01 April 2015
Primary: 35L65, 35Q35; Secondary: 35Q31.

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.
- Incompressible limit,
- compressible Euler equations,
- hyperbolic conservation laws
Citation: Rinaldo M. Colombo, Graziano Guerra. A coupling between a non--linear 1D compressible--incompressible limit and the 1D $p$--system in the non smooth case[J]. Networks and Heterogeneous Media, 2016, 11(2): 313-330. doi: 10.3934/nhm.2016.11.313

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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.

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