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Entropy boundary and jump conditions in the theory of sedimentation with compression
Author(s) -
Bürger R.,
Wendland W. L.
Publication year - 1998
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(199806)21:9<865::aid-mma983>3.0.co;2-9
Subject(s) - mathematics , classification of discontinuities , mathematical analysis , boundary value problem , entropy (arrow of time) , jump , thermodynamics , physics , quantum mechanics
We present an initial–boundary value problem of a quasilinear degenerate parabolic equation for the settling and consolidation of a flocculated suspension. The corresponding definition of generalized solutions is formulated. It is based on an entropy integral inequality in the sense of Kružkov. From this definition, jump and entropy conditions that have to be satisfied at discontinuities, and an entropy condition valid on one boundary of the computational domain are derived. The latter implies a set‐valued reformulation of the original boundary condition. It is interpreted geometrically and characterized by the solution of an auxiliary hyperbolic Riemann problem. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons, Ltd.