ASYMPTOTIC RAREFACTION WAVES FOR BALANCE LAWS WITH STIFF SOURCES

作     者：W. Lambert D. Marchesin 

作者机构：1-Instituto Nacional de Matemtica Pura e Aplicada Estrada Dona Castorina 11022460-320 Rio de Janeiro RJ Brazil Instituto de Matemtica Pura e Aplicada Estrada Dona Castorina 11022460-320 Rio de Janeiro RJ Brazil 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2009年第29卷第6期

页      面：1613-1628页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

基　　金：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 underCTPETRO Grant 21.01.0248.00 PETROBRAS under CTPETRO Grant 650.4.039.01.0, Brazil 

主　　题：balance laws asymptotic expansion rarefaction waves compositional models 

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.