Asymptotic study of the initial value problem to a standard one pressure model of multifluid flows in nondivergence form

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• 作者：M. Colombeau ^{mcolombeau@ime.usp.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35D30 ; 35F25 ; 65M06 ; 76-XX
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 January 2016
• 年：2016
• 卷：260
• 期：1
• 页码：197-217
• 全文大小：674 K

文摘

We construct families of approximate solutions to the initial value problem and provide complete mathematical proofs that they tend to satisfy the standard system of isothermal one pressure two-fluid flows in 1-D when the data are d30c6fefe1dda" title="Click to view the MathML source">L¹$L^1$ in densities and L^∞$L^{\infty }$ in velocities. To this end, we use a method that reduces this system of PDEs to a family of systems of four ODEs in Banach spaces whose smooth solutions are these approximate solutions. This method is constructive: using standard numerical methods for ODEs one can easily and accurately compute these approximate solutions which, therefore, from the mathematical proof, can serve for comparison with numerical schemes. One observes agreement with previously known solutions from scientific computing (Evje and Flatten, 2003 [16]) We show that one recovers the solutions of these authors (exactly in one case, with a slight difference in another case). Then we propose an efficient numerical scheme for the original system of two-fluid flows and show it gives back exactly the same results as the theoretical solutions obtained above.