ASYMPTOTIC RAREFACTION WAVES FOR BALANCE LAWS WITH STIFF SOURCES

doi:10.1016/S0252-9602(10)60005-7

数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (6): 1613-1628.doi: 10.1016/S0252-9602(10)60005-7

ASYMPTOTIC RAREFACTION WAVES FOR BALANCE LAWS WITH STIFF SOURCES

W. Lambert, D. Marchesin

1-Instituto Nacional de Matematica Pura e Aplicada, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJ, Brazil|Instituto de Matem\'atica Pura e Aplicada, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJ, Brazil

收稿日期:2009-10-25 出版日期:2009-11-20 发布日期:2009-11-20
基金资助:
This work was supported in part by: CNPq under grant 141573/2002-3, ANP/PRH-32, CNPq under Grant 301532/2003-6, FAPERJ
under Grant E-26/152.163/2002, FINEP under CTPETRO Grant 21.01.0248.00, PETROBRAS under CTPETRO Grant 650.4.039.01.0, Brazil.

ASYMPTOTIC RAREFACTION WAVES FOR BALANCE LAWS WITH STIFF SOURCES

W. Lambert, D. Marchesin

1-Instituto Nacional de Matematica Pura e Aplicada, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJ, Brazil|Instituto de Matem\'atica Pura e Aplicada, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJ, Brazil

Received:2009-10-25 Online:2009-11-20 Published:2009-11-20
Supported by:
This work was supported in part by: CNPq under grant 141573/2002-3, ANP/PRH-32, CNPq under Grant 301532/2003-6, FAPERJ
under Grant E-26/152.163/2002, FINEP under CTPETRO Grant 21.01.0248.00, PETROBRAS under CTPETRO Grant 650.4.039.01.0, Brazil.

摘要/Abstract

摘要：

We study the long time formation of rarefaction waves appearing in balance laws by means of singular perturbation methods. The balance laws are non standard because they contain a variable u that appears only in the flux terms. We present a concrete example occurring in flow of steam, nitrogen and water in porous media and an abstract example for a class of systems of three equations. In the concrete example the zero-order equations resulting from the expansion yield a type of conservation law system called compositional model in Petroleum Engineering. In this work we show how compositional models originate from physically more fundamental systems of balance laws. Under appropriate conditions, we prove that certain solutions of the system of balance laws decay with time to rarefaction wave solutions in the compositional model originating from the system of balance laws.

关键词: balance laws, asymptotic expansion, rarefaction waves, compositional models

Abstract:

Key words: balance laws, asymptotic expansion, rarefaction waves, compositional models

中图分类号:

35L65

W. Lambert, D. Marchesin. ASYMPTOTIC RAREFACTION WAVES FOR BALANCE LAWS WITH STIFF SOURCES[J]. 数学物理学报(英文版), 2009, 29(6): 1613-1628.

W. Lambert, D. Marchesin. ASYMPTOTIC RAREFACTION WAVES FOR BALANCE LAWS WITH STIFF SOURCES[J]. Acta mathematica scientia,Series B, 2009, 29(6): 1613-1628.

参考文献

[1] Bruining J, Marchesin D. Nitrogen and steam injection in a porous medium with water. Transport in Porous Media, 2006, 62(3): 251--281

[2] Bruining J, Marchesin D, Van Duijn C J. Steam injection into water-saturated porous rock. Comput Appl Math, 2003, 22(3): 359--395

[3] Bruining J, Marchesin D. Maximal oil recovery by simultaneous condensation alkane and steam. Phys Rev E, 2007

[4] Chen G Q, Levermore C D, Liu T P. Hyperbolic conservations laws with stiff relaxation terms and entropy. Comm Pure Appl Math, 1994, 47: 787--830

[5] Fan H, Luo T. Convergence to equilibrium rarefaction waves for discontinuous solutions of shallow water wave equations with relaxation. Quat Appl Math, 2005, 63(3): 575--600

[6] Hirasaki G. Application of the theory of multicomponent multiphase displacement to three component, two phase surfactant flooding. Soc Petr Eng J, 1981, 21(2): 191--204

[7] Hsiao L, Pan R. Zero relaxation limit to centered rarefaction waves for a rate-type viscoelastic system. J Differ Equ, 1999, 157: 20--40

[8] John F. Partial Differential Equations. 3rd. New York: Springer-Verlag, 1978

[9] Kevorkian J K, Cole J D. Multiple Scale and Singular Perturbation Methods. New York: Springer-Verlag, 2000

[10] Kawashima S, Yong W. Decay estimates for hyperbolic balance laws. Z Anal Anwend, 2009, 28(1): 1--33

[11] Lake L W. Enhanced Oil Recovery. Prentice Hall, 1989

[12] Lambert W, Marchesin D. The Riemann problem for compositional flows in porous media with mass transfer between phases. to appear in Journal of Hyperbolic Equations, 2009

[13] Lambert W, Marchesin D, Bruining J. The Riemann solution for the injection of steam and nitrogen in a porous medium. to appear in to Transport in Porous Media, 2009

[14] Liu T P. Hyperbolic conservation laws with relaxation. Comm Math Phy, 1987, 108(1): 153--175

[15] Natalini R. Recent results on hyperbolic relaxation problems Analysis of systems of conservation laws, Chapman and Hall/CRC Monogr Surv Pure Appl Math, 99. Boca Raton, FL: Chapman and Hall/CRC, 1999: 128--198

[16] Pope G A, Nelson R C. A chemical flooding compositional simulator. Soc Petr Eng J, 1978, 18(5): 339--354

[17] Yong W A. Singular Perturbations of First-Order Hyperbolic Systems with Stiff Source Terms. J Differ Equ, 1999, 155(1): 89--132

[18] Zhao H, Zhao Y. Convergence to strong nonlinear rarefaction waves for global smooth solutions of p-system with relaxation. Disc and Cont Dyn Syst, 2003, 9(5): 1243--1262

ASYMPTOTIC RAREFACTION WAVES FOR BALANCE LAWS WITH STIFF SOURCES

ASYMPTOTIC RAREFACTION WAVES FOR BALANCE LAWS WITH STIFF SOURCES

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