메뉴 건너뛰기




Volumn 17, Issue 3, 2006, Pages 257-292

On an extended clarifier-thickener model with singular source and sink terms

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33750354897     PISSN: 09567925     EISSN: 14694425     Source Type: Journal    
DOI: 10.1017/S0956792506006619     Document Type: Article
Times cited : (16)

References (54)
  • 2
    • 1642367583 scopus 로고    scopus 로고
    • Godunov-type approximation for a general resonant balance law with large data
    • AMADORI, D., GOSSE, L. & GUERRA, G. (2004) Godunov-type approximation for a general resonant balance law with large data. J. Differential Equations, 198, 233-274.
    • (2004) J. Differential Equations , vol.198 , pp. 233-274
    • Amadori, D.1    Gosse, L.2    Guerra, G.3
  • 3
    • 17744396698 scopus 로고    scopus 로고
    • Uniqueness for a scalar conservation law with discontinuous flux via adapted entropies
    • AUDUSSE, E. & PERTHAME, B. (2005) Uniqueness for a scalar conservation law with discontinuous flux via adapted entropies. Proc. Royal Soc. Edinburgh Sect. A, 135, 253-265.
    • (2005) Proc. Royal Soc. Edinburgh Sect. A , vol.135 , pp. 253-265
    • Audusse, E.1    Perthame, B.2
  • 4
    • 33644811017 scopus 로고    scopus 로고
    • Existence and uniqueness of entropy solution of scalar conservation laws with a flux function involving discontinuous coefficients
    • BACHMANN, F. & VOVELLE, J. (2006) Existence and uniqueness of entropy solution of scalar conservation laws with a flux function involving discontinuous coefficients. Comm. Partial Differential Equations, 31, 371-395.
    • (2006) Comm. Partial Differential Equations , vol.31 , pp. 371-395
    • Bachmann, F.1    Vovelle, J.2
  • 5
    • 12144290908 scopus 로고    scopus 로고
    • Strongly degenerate parabolichyperbolic systems modeling polydisperse sedimentation with compression
    • BERRES, S., BÜRGER, R., KARLSEN, K. H. & TORY, E. M. (2003) Strongly degenerate parabolichyperbolic systems modeling polydisperse sedimentation with compression. SIAM J. Appl. Math., 64, 41-80.
    • (2003) SIAM J. Appl. Math. , vol.64 , pp. 41-80
    • Berres, S.1    Bürger, R.2    Karlsen, K.H.3    Tory, E.M.4
  • 6
    • 1442265049 scopus 로고    scopus 로고
    • Central schemes and systems of conservation laws with discontinuous coefficients modeling gravity separation of polydisperse suspensions
    • BERRES, S., BÜRGER, R. & KARLSEN, K.H. (2004) Central schemes and systems of conservation laws with discontinuous coefficients modeling gravity separation of polydisperse suspensions. J. Comp. Appl. Math., 164-165, 53-80.
    • (2004) J. Comp. Appl. Math. , vol.164-165 , pp. 53-80
    • Berres, S.1    Bürger, R.2    Karlsen, K.H.3
  • 7
    • 0032092187 scopus 로고    scopus 로고
    • One-dimensional transport equations with discontinuous coefficients
    • BOUCHUT, F. & JAMES, F. (1998) One-dimensional transport equations with discontinuous coefficients. Nonlinear Anal., 32, 891-933.
    • (1998) Nonlinear Anal. , vol.32 , pp. 891-933
    • Bouchut, F.1    James, F.2
  • 8
    • 0442323025 scopus 로고    scopus 로고
    • On a diffusively corrected kinematic-wave traffic flow model with changing road surface conditions
    • BÜRGER, R. & KARLSEN, K.H. (2003) On a diffusively corrected kinematic-wave traffic flow model with changing road surface conditions. Math. Models Methods Appl. Sci., 13, 1767-1799.
    • (2003) Math. Models Methods Appl. Sci. , vol.13 , pp. 1767-1799
    • Bürger, R.1    Karlsen, K.H.2
  • 9
    • 0037412050 scopus 로고    scopus 로고
    • A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units
    • BÜRGER, R., KARLSEN, K. H., KLINGENBERG, C. & RISEBRO, N. H. (2003) A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units. Nonlin. Anal. Real World Appl., 4, 457-481.
    • (2003) Nonlin. Anal. Real World Appl. , vol.4 , pp. 457-481
    • Bürger, R.1    Karlsen, K.H.2    Klingenberg, C.3    Risebro, N.H.4
  • 11
    • 0942267324 scopus 로고    scopus 로고
    • Numerical methods for the simulation of continuous sedimentation in ideal clarifier-thickener units
    • BÜRGER, R., KARLSEN, K. H., RISEBRO, N. H. & TOWERS, J. D. (2004) Numerical methods for the simulation of continuous sedimentation in ideal clarifier-thickener units. Int. J. Mineral Process., 73, 209-228.
    • (2004) Int. J. Mineral Process. , vol.73 , pp. 209-228
    • Bürger, R.1    Karlsen, K.H.2    Risebro, N.H.3    Towers, J.D.4
  • 12
    • 18344418212 scopus 로고    scopus 로고
    • t and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units
    • t and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units. Numer. Math., 97, 25-65.
    • (2004) Numer. Math. , vol.97 , pp. 25-65
    • Bürger, R.1    Karlsen, K.H.2    Risebro, N.H.3    Towers, J.D.4
  • 13
    • 33746244792 scopus 로고    scopus 로고
    • Closed-form and finite difference solutions to a population balance model of grinding mills
    • BÜRGER, R., KARLSEN, K. H. & TOWERS, J. D. (2005) Closed-form and finite difference solutions to a population balance model of grinding mills. J. Eng. Math., 51, 165-195.
    • (2005) J. Eng. Math. , vol.51 , pp. 165-195
    • Bürger, R.1    Karlsen, K.H.2    Towers, J.D.3
  • 14
    • 21244495710 scopus 로고    scopus 로고
    • A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units
    • BÜRGER, R., KARLSEN, K. H. & TOWERS, J. D. (2005) A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units. SIAM J. Appl. Math., 65, 882-940.
    • (2005) SIAM J. Appl. Math. , vol.65 , pp. 882-940
    • Bürger, R.1    Karlsen, K.H.2    Towers, J.D.3
  • 15
    • 24144462481 scopus 로고    scopus 로고
    • Mathematical model and numerical simulation of the dynamics of flocculated suspensions in clarifier-thickeners
    • BÜRGER, R., KARLSEN, K. H. & TOWERS, J. D. (2005) Mathematical model and numerical simulation of the dynamics of flocculated suspensions in clarifier-thickeners. Chem. Eng. J., 111, 119-134.
    • (2005) Chem. Eng. J. , vol.111 , pp. 119-134
    • Bürger, R.1    Karlsen, K.H.2    Towers, J.D.3
  • 17
    • 33750364723 scopus 로고    scopus 로고
    • A hyperbolic system of conservation laws in modeling endovascular treatment of abdominal aortic aneurysm
    • Freistühler, H. and Warnecke, G. (eds.), February/March Volume I. International Series of Numerical Mathematics Birkḧuser Verlag, Basel
    • ČANIĆ, S. & MIRKOVIĆ, D. (2001) A hyperbolic system of conservation laws in modeling endovascular treatment of abdominal aortic aneurysm. In: Freistühler, H. and Warnecke, G. (eds.), Hyperbolic Problems: Theory, Numerics, Applications. Eighth International Conference in Magdeburg, February/March 2000, Volume I. International Series of Numerical Mathematics 140, Birkḧuser Verlag, Basel, 227-236.
    • (2000) Hyperbolic Problems: Theory, Numerics, Applications. Eighth International Conference in Magdeburg , vol.140 , pp. 227-236
    • Čanić, S.1    Mirković, D.2
  • 18
    • 84966217981 scopus 로고
    • Monotone difference approximations for scalar conservation laws
    • CRANDALL, M. G. & MAJDA, A. (1980) Monotone difference approximations for scalar conservation laws. Math. Comp., 34, 1-21.
    • (1980) Math. Comp. , vol.34 , pp. 1-21
    • Crandall, M.G.1    Majda, A.2
  • 19
    • 0001291913 scopus 로고
    • On scalar conservation laws with point source and discontinuous flux function
    • DIEHL, S. (1995) On scalar conservation laws with point source and discontinuous flux function. SIAM J. Math. Anal., 26, 1425-1451.
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 1425-1451
    • Diehl, S.1
  • 20
    • 0030127106 scopus 로고    scopus 로고
    • A conservation law with point source and discontinuous flux function modelling continuous sedimentation
    • DIEHL, S. (1996) A conservation law with point source and discontinuous flux function modelling continuous sedimentation. SIAM J. Appl. Math., 56, 388-419.
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 388-419
    • Diehl, S.1
  • 21
    • 0030529879 scopus 로고    scopus 로고
    • Scalar conservation laws with discontinuous flux function: I. The viscous profile condition
    • DIEHL, S. (1996) Scalar conservation laws with discontinuous flux function: I. The viscous profile condition. Commun. Math. Phys., 176, 23-44.
    • (1996) Commun. Math. Phys. , vol.176 , pp. 23-44
    • Diehl, S.1
  • 22
    • 0031209077 scopus 로고    scopus 로고
    • Dynamic and steady-state behaviour of continuous sedimentation
    • DIEHL, S. (1997) Dynamic and steady-state behaviour of continuous sedimentation. SIAM J. Appl. Math., 57, 991-1018.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 991-1018
    • Diehl, S.1
  • 23
    • 0034352369 scopus 로고    scopus 로고
    • On boundary conditions and solutions for ideal clarifier-thickener units
    • DIEHL, S. (2000) On boundary conditions and solutions for ideal clarifier-thickener units. Chem. Eng. J., 80, 119-133.
    • (2000) Chem. Eng. J. , vol.80 , pp. 119-133
    • Diehl, S.1
  • 24
    • 0035498941 scopus 로고    scopus 로고
    • Operating charts for continuous sedimentation I: Control of steady states
    • DIEHL, S. (2001) Operating charts for continuous sedimentation I: Control of steady states. J. Eng. Math., 41, 117-144.
    • (2001) J. Eng. Math. , vol.41 , pp. 117-144
    • Diehl, S.1
  • 25
    • 0030530103 scopus 로고    scopus 로고
    • Scalar conservation laws with discontinuous flux function: II. On the stability of the viscous profiles
    • DIEHL, S. & WALLIN, N.-O. (1996) Scalar conservation laws with discontinuous flux function: II. On the stability of the viscous profiles. Commun. Math. Phys., 176, 45-71.
    • (1996) Commun. Math. Phys. , vol.176 , pp. 45-71
    • Diehl, S.1    Wallin, N.-O.2
  • 26
    • 84966208277 scopus 로고
    • One-sided difference approximations for nonlinear conservation laws
    • ENGQUIST, B. & OSHER, S. (1981) One-sided difference approximations for nonlinear conservation laws. Math. Comp., 36, 321-351.
    • (1981) Math. Comp. , vol.36 , pp. 321-351
    • Engquist, B.1    Osher, S.2
  • 27
    • 9644289644 scopus 로고    scopus 로고
    • Performance of the reflux classifier for gravity separation at full scale
    • GALVIN, K. P., CALLEN, A., ZHOU, J. & DOROODCHI, E. (2005) Performance of the reflux classifier for gravity separation at full scale. Minerals Eng., 18, 19-24.
    • (2005) Minerals Eng. , vol.18 , pp. 19-24
    • Galvin, K.P.1    Callen, A.2    Zhou, J.3    Doroodchi, E.4
  • 29
    • 0037155746 scopus 로고    scopus 로고
    • Influence of parallel plates in a liquid fluidized bed system
    • GALVIN, K. P. & NGUYENTRANLAM, G. (2002) Influence of parallel plates in a liquid fluidized bed system. Chem. Eng. Sci., 57, 1231-1234.
    • (2002) Chem. Eng. Sci. , vol.57 , pp. 1231-1234
    • Galvin, K.P.1    Nguyentranlam, G.2
  • 30
    • 21144479253 scopus 로고
    • Conservation laws with discontinuous flux functions
    • GIMSE, T. (1993) Conservation laws with discontinuous flux functions. SIAM J. Math. Anal., 24, 279-289.
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 279-289
    • Gimse, T.1
  • 31
    • 0001367271 scopus 로고
    • Solution of the Cauchy problem for a conservation law with a discontinuous Flux function
    • GIMSE, T. & RISEBRO, N. H. (1992) Solution of the Cauchy problem for a conservation law with a discontinuous Flux function. SIAM J. Math. Anal., 23, 635-648.
    • (1992) SIAM J. Math. Anal. , vol.23 , pp. 635-648
    • Gimse, T.1    Risebro, N.H.2
  • 32
    • 40749159424 scopus 로고
    • High resolution schemes for hyperbolic conservation laws
    • HARTEN, A. (1983) High resolution schemes for hyperbolic conservation laws. J. Comp. Phys., 49, 357-393.
    • (1983) J. Comp. Phys. , vol.49 , pp. 357-393
    • Harten, A.1
  • 33
    • 0032882326 scopus 로고    scopus 로고
    • Solving the Buckley-Leverett equation with gravity in a heterogeneous porous medium
    • KAASSCHIETER, E. F. (1999) Solving the Buckley-Leverett equation with gravity in a heterogeneous porous medium. Comput. Geosci., 3, 23-48.
    • (1999) Comput. Geosci. , vol.3 , pp. 23-48
    • Kaasschieter, E.F.1
  • 34
    • 2942692254 scopus 로고    scopus 로고
    • A relaxation scheme for conservation laws with a discontinuous coefficient
    • KARLSEN, K. H., KLINGENBERG, C. & RISEBRO, N. H. (2003) A relaxation scheme for conservation laws with a discontinuous coefficient. Math. Comp. 73, 1235-1259.
    • (2003) Math. Comp. , vol.73 , pp. 1235-1259
    • Karlsen, K.H.1    Klingenberg, C.2    Risebro, N.H.3
  • 35
    • 4444234405 scopus 로고    scopus 로고
    • 1 stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients
    • 49 pp.
    • 1 stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients. Skr. K. Nor. Vid. Selsk., 49 pp.
    • (2003) Skr. K. Nor. Vid. Selsk.
    • Karlsen, K.H.1    Risebro, N.H.2    Towers, J.D.3
  • 36
    • 4444361444 scopus 로고    scopus 로고
    • Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux
    • KARLSEN, K. H. & TOWERS, J. D. (2004) Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux. Chin. Ann. Math., 25B, 287-318.
    • (2004) Chin. Ann. Math. , vol.25 B , pp. 287-318
    • Karlsen, K.H.1    Towers, J.D.2
  • 37
    • 0033196472 scopus 로고    scopus 로고
    • Stability of conservation laws with discontinuous coefficients
    • KLAUSEN, R. A. & RISEBRO, N. H. (1999) Stability of conservation laws with discontinuous coefficients. J. Diff. Eqns., 157, 41-60.
    • (1999) J. Diff. Eqns. , vol.157 , pp. 41-60
    • Klausen, R.A.1    Risebro, N.H.2
  • 39
    • 84956238079 scopus 로고
    • First order quasilinear equations in several independent variables
    • KRUŽKOV, S. N. (1970) First order quasilinear equations in several independent variables. Math. USSR Sb., 10, 217-243.
    • (1970) Math. USSR Sb. , vol.10 , pp. 217-243
    • Kružkov, S.N.1
  • 40
    • 0010086308 scopus 로고
    • A theory of sedimentation
    • KYNCH, G. J. (1952) A theory of sedimentation. Trans. Faraday Soc., 48, 166-176.
    • (1952) Trans. Faraday Soc. , vol.48 , pp. 166-176
    • Kynch, G.J.1
  • 41
    • 33646482469 scopus 로고    scopus 로고
    • Convergence of upwind finite difference schemes for a scalar conservation law with indefinite discontinuities in the flux function
    • MISHRA, S. (2005) Convergence of upwind finite difference schemes for a scalar conservation law with indefinite discontinuities in the flux function. SIAM J. Numer. Anal., 43, 559-577.
    • (2005) SIAM J. Numer. Anal. , vol.43 , pp. 559-577
    • Mishra, S.1
  • 42
    • 0039960089 scopus 로고
    • An analysis of the traffic on highways with changing road surface conditions
    • MOCHON, S. (1987) An analysis of the traffic on highways with changing road surface conditions. Math. Modelling, 9, 1-11.
    • (1987) Math. Modelling , vol.9 , pp. 1-11
    • Mochon, S.1
  • 43
    • 0025114944 scopus 로고
    • Continuous gravity separation of concentrated bidisperse suspensions in a vertical column
    • NASR-EL-DIN, H., MASLIYAH, J. H. & NANDAKUMAR, K. (1990) Continuous gravity separation of concentrated bidisperse suspensions in a vertical column. Chem. Eng. Sci., 45, 849-857.
    • (1990) Chem. Eng. Sci. , vol.45 , pp. 849-857
    • Nasr-El-Din, H.1    Masliyah, J.H.2    Nandakumar, K.3
  • 44
    • 0033201404 scopus 로고    scopus 로고
    • Continuous separation of suspensions containing light and heavy particle species
    • NASR-EL-DIN, H., MASLIYAH, J. H. & NANDAKUMAR, K. (1999) Continuous separation of suspensions containing light and heavy particle species. Canad. J. Chem. Eng., 77, 1003-1012.
    • (1999) Canad. J. Chem. Eng. , vol.77 , pp. 1003-1012
    • Nasr-El-Din, H.1    Masliyah, J.H.2    Nandakumar, K.3
  • 45
    • 38249031459 scopus 로고
    • Continuous gravity separation of a bidisperse suspension in a vertical column
    • NASR-EL-DIN, H., MASLIYAH, J. H., NANDAKUMAR, K. & LAW, D. H.-S. (1988) Continuous gravity separation of a bidisperse suspension in a vertical column. Chem. Eng. Sci., 43, 3225-3234.
    • (1988) Chem. Eng. Sci. , vol.43 , pp. 3225-3234
    • Nasr-El-Din, H.1    Masliyah, J.H.2    Nandakumar, K.3    Law, D.H.-S.4
  • 46
    • 0035444264 scopus 로고    scopus 로고
    • Particle classiffication in the reflux classifier
    • NGUYENTRANLAM, G. & GALVIN, K. P. (2001) Particle classiffication in the reflux classifier. Minerals Eng., 14, 1081-1091.
    • (2001) Minerals Eng. , vol.14 , pp. 1081-1091
    • Nguyentranlam, G.1    Galvin, K.P.2
  • 47
    • 0037053703 scopus 로고    scopus 로고
    • Solutions of Hamilton-Jacobi equations and scalar conservation laws with discontinuous space-time dependence
    • OSTROV, D. (2002) Solutions of Hamilton-Jacobi equations and scalar conservation laws with discontinuous space-time dependence, J. Differential Equations, 182, 51-77.
    • (2002) J. Differential Equations , vol.182 , pp. 51-77
    • Ostrov, D.1
  • 49
    • 84990622706 scopus 로고
    • Two new moving boundary problems for scalar conservation laws
    • ROSS, D. S. (1988) Two new moving boundary problems for scalar conservation laws. Comm. Pure Appl. Math., 41, 725-737.
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 725-737
    • Ross, D.S.1
  • 50
    • 0037295910 scopus 로고    scopus 로고
    • Analysis and approximation of a scalar conservation law with a flux function with discontinuous coefficients
    • SEGUIN, N. & VOVELLE, J. (2003) Analysis and approximation of a scalar conservation law with a flux function with discontinuous coefficients. Math. Models Meth. Appl. Sci., 13, 221-257.
    • (2003) Math. Models Meth. Appl. Sci. , vol.13 , pp. 221-257
    • Seguin, N.1    Vovelle, J.2
  • 52
    • 0034449655 scopus 로고    scopus 로고
    • Convergence of a difference scheme for conservation laws with a discontinuous flux
    • TOWERS, J. D. (2000) Convergence of a difference scheme for conservation laws with a discontinuous flux. SIAM J. Numer. Anal., 38, 681-698.
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 681-698
    • Towers, J.D.1
  • 53
    • 0035453016 scopus 로고    scopus 로고
    • A difference scheme for conservation laws with a discontinuous flux: The nonconvex case
    • TOWERS, J. D. (2001) A difference scheme for conservation laws with a discontinuous flux: The nonconvex case. SIAM J. Numer. Anal., 39, 1197-1218.
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 1197-1218
    • Towers, J.D.1
  • 54
    • 0029412586 scopus 로고
    • Effects of capillary forces on immiscible two-phase flow in strongly hetereogeneous porous media
    • VAN DUIJN, C. J., DE NEEF, M. J. & MOLENAAR, J. (1995) Effects of capillary forces on immiscible two-phase flow in strongly hetereogeneous porous media. Transp. Porous Media, 21, 71-93.
    • (1995) Transp. Porous Media , vol.21 , pp. 71-93
    • Van Duijn, C.J.1    De Neef, M.J.2    Molenaar, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.