Non‐selfsimilar global solutions to a two‐dimensional system of conservation laws |
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| Authors: | Yicheng Pang Jinhuan Wang Yuanying Zhao |
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| Affiliation: | 1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, China;2. Department of Mathematics and Information Science, Tangshan Normal University, Tangshan, China;3. College of Mathematics and Information Science, Guiyang University, Guiyang, China |
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| Abstract: | 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. |
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| Keywords: | systems of conservation laws two‐dimensional Riemann problem non‐selfsimilar global solutions |
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