On the uniqueness of vanishing viscosity solutions for Riemann problems for polymer flooding

On the uniqueness of vanishing viscosity solutions for Riemann problems for polymer flooding We consider the vanishing viscosity solutions of Riemann problems for polymer flooding models. The models reduce to triangular systems of conservation laws in a suitable Lagrangian coordinate, which connects to scalar conservation laws with discontinuous flux. These systems are parabolic degenerate along certain curves in the domain. A vanishing viscosity solution based on a partially viscous model is given in a parallell paper (Guerra and Shen in Partial Differ Equ Math Phys Stoch Anal: 2017). In this paper the fully viscous model is treated. Through several counter examples we show that, as the ratio of the viscosity parameters varies, infinitely many vanishing viscosity limit solutions can be constructed. Under some further monotonicity assumptions, the uniqueness of vanishing viscosity solutions for Riemann problems can be proved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Differential Equations and Applications NoDEA Springer Journals

On the uniqueness of vanishing viscosity solutions for Riemann problems for polymer flooding

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Mathematics; Analysis
ISSN
1021-9722
eISSN
1420-9004
D.O.I.
10.1007/s00030-017-0461-y
Publisher site
See Article on Publisher Site

Abstract

We consider the vanishing viscosity solutions of Riemann problems for polymer flooding models. The models reduce to triangular systems of conservation laws in a suitable Lagrangian coordinate, which connects to scalar conservation laws with discontinuous flux. These systems are parabolic degenerate along certain curves in the domain. A vanishing viscosity solution based on a partially viscous model is given in a parallell paper (Guerra and Shen in Partial Differ Equ Math Phys Stoch Anal: 2017). In this paper the fully viscous model is treated. Through several counter examples we show that, as the ratio of the viscosity parameters varies, infinitely many vanishing viscosity limit solutions can be constructed. Under some further monotonicity assumptions, the uniqueness of vanishing viscosity solutions for Riemann problems can be proved.

Journal

Nonlinear Differential Equations and Applications NoDEASpringer Journals

Published: Jun 15, 2017

References

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