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A coupling between a non--linear 1D compressible--incompressible limit and the 1D $p$--system in the non smooth case
1. | INdAM Unit c/o DII, Università degli Studi di Brescia, Via Branze 38, 25123 Brescia, Italy |
2. | Dipartimento di Matematica e Applicazioni Via Roberto Cozzi, 55 - 20125 Milano, Italy |
References:
[1] |
D. Amadori and G. Guerra, Global BV solutions and relaxation limit for a system of conservation laws, Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 1-26.
doi: 10.1017/S0308210500000767. |
[2] |
R. Borsche, R. M. Colombo and M. Garavello, Mixed systems: ODEs - balance laws, J. Differential Equations, 252 (2012), 2311-2338.
doi: 10.1016/j.jde.2011.08.051. |
[3] |
A. Bressan, Hyperbolic Systems of Conservation Laws, vol. 20 of Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford, 2000, The one-dimensional Cauchy problem. |
[4] |
R. M. Colombo and G. Guerra, Bv solutions to 1d isentropic euler equations in the zero mach number limit, J. Hyperbolic Differ. Equ., 2016, to appear. |
[5] |
R. M. Colombo, G. Guerra and V. Schleper, The compressible to incompressible limit of one dimensional euler equations: The non smooth case, Arch. Ration. Mech. Anal., 219 (2016), 701-718.
doi: 10.1007/s00205-015-0904-8. |
[6] |
R. M. Colombo and V. Schleper, Two-phase flows: Non-smooth well posedness and the compressible to incompressible limit, Nonlinear Anal. Real World Appl., 13 (2012), 2195-2213.
doi: 10.1016/j.nonrwa.2012.01.015. |
[7] |
S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math., 34 (1981), 481-524.
doi: 10.1002/cpa.3160340405. |
[8] |
S. Klainerman and A. Majda, Compressible and incompressible fluids, Comm. Pure Appl. Math., 35 (1982), 629-651.
doi: 10.1002/cpa.3160350503. |
[9] |
G. Métivier and S. Schochet, The incompressible limit of the non-isentropic Euler equations, Arch. Ration. Mech. Anal., 158 (2001), 61-90.
doi: 10.1007/PL00004241. |
[10] |
S. Schochet, The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit, Comm. Math. Phys., 104 (1986), 49-75.
doi: 10.1007/BF01210792. |
[11] |
S. Schochet, The mathematical theory of low Mach number flows, M2AN Math. Model. Numer. Anal., 39 (2005), 441-458.
doi: 10.1051/m2an:2005017. |
[12] |
J. Xu and W.-A. Yong, A note on incompressible limit for compressible Euler equations, Math. Methods Appl. Sci., 34 (2011), 831-838.
doi: 10.1002/mma.1405. |
show all references
References:
[1] |
D. Amadori and G. Guerra, Global BV solutions and relaxation limit for a system of conservation laws, Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 1-26.
doi: 10.1017/S0308210500000767. |
[2] |
R. Borsche, R. M. Colombo and M. Garavello, Mixed systems: ODEs - balance laws, J. Differential Equations, 252 (2012), 2311-2338.
doi: 10.1016/j.jde.2011.08.051. |
[3] |
A. Bressan, Hyperbolic Systems of Conservation Laws, vol. 20 of Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford, 2000, The one-dimensional Cauchy problem. |
[4] |
R. M. Colombo and G. Guerra, Bv solutions to 1d isentropic euler equations in the zero mach number limit, J. Hyperbolic Differ. Equ., 2016, to appear. |
[5] |
R. M. Colombo, G. Guerra and V. Schleper, The compressible to incompressible limit of one dimensional euler equations: The non smooth case, Arch. Ration. Mech. Anal., 219 (2016), 701-718.
doi: 10.1007/s00205-015-0904-8. |
[6] |
R. M. Colombo and V. Schleper, Two-phase flows: Non-smooth well posedness and the compressible to incompressible limit, Nonlinear Anal. Real World Appl., 13 (2012), 2195-2213.
doi: 10.1016/j.nonrwa.2012.01.015. |
[7] |
S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math., 34 (1981), 481-524.
doi: 10.1002/cpa.3160340405. |
[8] |
S. Klainerman and A. Majda, Compressible and incompressible fluids, Comm. Pure Appl. Math., 35 (1982), 629-651.
doi: 10.1002/cpa.3160350503. |
[9] |
G. Métivier and S. Schochet, The incompressible limit of the non-isentropic Euler equations, Arch. Ration. Mech. Anal., 158 (2001), 61-90.
doi: 10.1007/PL00004241. |
[10] |
S. Schochet, The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit, Comm. Math. Phys., 104 (1986), 49-75.
doi: 10.1007/BF01210792. |
[11] |
S. Schochet, The mathematical theory of low Mach number flows, M2AN Math. Model. Numer. Anal., 39 (2005), 441-458.
doi: 10.1051/m2an:2005017. |
[12] |
J. Xu and W.-A. Yong, A note on incompressible limit for compressible Euler equations, Math. Methods Appl. Sci., 34 (2011), 831-838.
doi: 10.1002/mma.1405. |
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