TY - JOUR
T1 - On the Cauchy problems for polymer flooding with gravitation
AU - Shen, Wen
N1 - Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/7/5
Y1 - 2016/7/5
N2 - We study two systems of conservation laws for polymer flooding in secondary oil recovery, one with gravitation force and one without. For each model, we prove global existence of weak solutions for the Cauchy problems, under rather general assumptions on the flux functions. Approximate solutions are constructed through a front tracking algorithm, and compactness is achieved through the bound on suitably defined wave strengths. As the main technical novelty, we introduce some new nonlinear functionals that yield a uniform bound on the total variation of the flux function.
AB - We study two systems of conservation laws for polymer flooding in secondary oil recovery, one with gravitation force and one without. For each model, we prove global existence of weak solutions for the Cauchy problems, under rather general assumptions on the flux functions. Approximate solutions are constructed through a front tracking algorithm, and compactness is achieved through the bound on suitably defined wave strengths. As the main technical novelty, we introduce some new nonlinear functionals that yield a uniform bound on the total variation of the flux function.
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U2 - 10.1016/j.jde.2016.03.020
DO - 10.1016/j.jde.2016.03.020
M3 - Article
AN - SCOPUS:84962360727
SN - 0022-0396
VL - 261
SP - 627
EP - 653
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 1
ER -