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Entropy boundary and jump conditions in the theory of sedimentation with compression

1998; Wiley; Volume: 21; Issue: 9 Linguagem: Inglês

10.1002/(sici)1099-1476(199806)21

1099-1476

Raimund Bürger, Wolfgang L. Wendland,

Nonlinear Partial Differential Equations

Mathematical Methods in the Applied SciencesVolume 21, Issue 9 p. 865-882 Research Article Entropy boundary and jump conditions in the theory of sedimentation with compression R. Bürger, R. Bürger Institute of Mathematics A, University of Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, GermanySearch for more papers by this authorW. L. Wendland, Corresponding Author W. L. Wendland Institute of Mathematics A, University of Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, GermanyInstitute of Mathematics A, University of Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany===Search for more papers by this author R. Bürger, R. Bürger Institute of Mathematics A, University of Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, GermanySearch for more papers by this authorW. L. Wendland, Corresponding Author W. L. Wendland Institute of Mathematics A, University of Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, GermanyInstitute of Mathematics A, University of Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany===Search for more papers by this author First published: 04 December 1998 https://doi.org/10.1002/(SICI)1099-1476(199806)21:9 3.0.CO;2-9Citations: 23AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract 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. References 1 Bardos, C., Le Roux, A. Y. and Nedelec, J. C., 'First order quasilinear equations with boundary conditions', Commun. 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