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Non‐selfsimilar global solutions to a two‐dimensional system of conservation laws
Author(s) -
Pang Yicheng,
Wang Jinhuan,
Zhao Yuanying
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4398
Subject(s) - conservation law , mathematics , riemann hypothesis , transformation (genetics) , constant (computer programming) , riemann problem , state (computer science) , nonlinear system , function (biology) , simple (philosophy) , mathematical analysis , calculus (dental) , physics , computer science , quantum mechanics , philosophy , algorithm , medicine , dentistry , biochemistry , chemistry , epistemology , evolutionary biology , biology , gene , programming language
This paper considers the two‐dimensional Riemann problem for a system of conservation laws that models the polymer flooding in an oil reservoir. The initial data are two different constant states separated by a smooth curve. By virtue of a nonlinear coordinate transformation, this problem is converted into another simple one. We then analyze rigorously the expressions of elementary waves. Based on these preparations, we obtain respectively four kinds of non‐selfsimilar global solutions and their corresponding criteria. It is shown that the intermediate state between two elementary waves is no longer a constant state and that the expression of the rarefaction wave is obtained by constructing an inverse function. These are distinctive features of the non‐selfsimilar global solutions. Copyright © 2017 John Wiley & Sons, Ltd.