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Analysis of a Non‐hyperbolic System Modeling Two‐phase Flows Part 1: The Effects of Diffusion and Relaxation
Author(s) -
Bedjaoui Nabil,
Sainsaulieu Lionel
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199706)20:9<783::aid-mma882>3.0.co;2-q
Subject(s) - conservation law , mathematics , relaxation (psychology) , diffusion , stability (learning theory) , norm (philosophy) , phase (matter) , mathematical analysis , statistical physics , thermodynamics , physics , law , computer science , psychology , social psychology , quantum mechanics , machine learning , political science
The paper considers the non‐linear stability of a non‐hyperbolic system of conservation laws with both relaxation and diffusion, which is commonly used for the modeling of two‐phase fluid flows. Global existence in time is proved for initial data with a sufficiently small H 1 norm. This result heavily depends on the nice structure of the relaxation system, derived from the initial system by setting the relaxation variables to zero. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.