Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 32, pp. 118.
Existence of solutions to the Riemann problem for a model of twophase flows
Mai Duc Thanh, Dao Huy Cuong
Abstract:
We study the existence of solutions of the Riemann problem for a model
of twophase flows. The model has the form of a nonconservative hyperbolic
system of balance laws. Based on a phase decomposition approach, we obtain
all the wave curves. By developing an analytic method, we can establish
a system of nonlinear algebraic equations for each solution of the
Riemann problem. The system is underdetermined and can be parameterized by
the volume fraction in one phase. Therefore, an argument relying on the
ImplicitFunction Theorem leads us to the existence of solutions of
the Riemann problem for the model for sufficiently large initial data.
Furthermore, the structure of the Riemann solutions obtained by this method
can also be obtained.
Submitted November 19, 2014. Published February 5, 2015.
Math Subject Classifications: 35L65, 35L67, 76T10, 76N10.
Key Words: Twophase flow; nonconservative; source term; jump relation;
shock; Riemann problem.
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Mai Duc Thanh
Department of Mathematics, International University
Vietnam National University  HCMC, Quarter 6
Linh Trung Ward, Thu Duc District
Ho Chi Minh City, Vietnam
email: mdthanh@hcmiu.edu.vn


Dao Huy Cuong
Nguyen Huu Cau High School, 07 Nguyen Anh Thu
Trung Chanh Ward, Hoc Mon District
Ho Chi Minh City, Vietnam
email: cuongnhc82@gmail.com

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