TY - JOUR

T1 - On the uniqueness of vanishing viscosity solutions for Riemann problems for polymer flooding

AU - Shen, Wen

N1 - Publisher Copyright:
© 2017, Springer International Publishing AG.

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s00030-017-0461-y

DO - 10.1007/s00030-017-0461-y

M3 - Article

AN - SCOPUS:85021112861

SN - 1021-9722

VL - 24

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

IS - 4

M1 - 37

ER -