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 f...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.展开更多
基金supported in part by: CNPq under grant 141573/2002-3,ANP/PRH-32CNPq under Grant 301532/2003-6+2 种基金FAPERJ under Grant E-26/152.163/2002FINEP underCTPETRO Grant 21.01.0248.00PETROBRAS under CTPETRO Grant 650.4.039.01.0, Brazil
文摘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.
