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Volumn 135, Issue 1, 2009, Pages 133-151

Stochastic particle approximation for measure valued solutions of the 2D Keller-Segel system

Author keywords

(Patlak )Keller Segel model; BBGKY hierarchy; Blow up; Chemotaxis; Stochastic interacting particles

Indexed keywords


EID: 67349094576     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9717-1     Document Type: Article
Times cited : (49)

References (21)
  • 1
    • 33747147890 scopus 로고    scopus 로고
    • The 8π-problem for radially symmetric solutions of a chemotaxis model in the plane
    • DOI 10.1002/mma.743
    • Biler, P., Karch, G., Laurencot, Ph., Nadzieja, T.: The 8π-problem for radially symmetric solutions of a chemotaxis model in the plane. Math. Methods Appl. Sci. 29, 1563-1583 (2006) (Pubitemid 44220492)
    • (2006) Mathematical Methods in the Applied Sciences , vol.29 , Issue.13 , pp. 1563-1583
    • Biler, P.1    Karch, G.2    Laurencot, P.3    Nadzieja, T.4
  • 2
    • 58149087814 scopus 로고    scopus 로고
    • Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions
    • Blanchet, A., Dolbeault, J., Perthame, B.: Two-dimensional Keller-Segel model: optimal critical mass and qualitative properties of the solutions. Electron. J. Differ. Equ. 44, 32 (2006)
    • (2006) Electron. J. Differ. Equ. , vol.44 , pp. 32
    • Blanchet, A.1    Dolbeault, J.2    Perthame, B.3
  • 3
    • 55549135711 scopus 로고    scopus 로고
    • Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model
    • 2
    • Blanchet, A., Calvez, V., Carrillo, J.A.: Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model. SIAM J. Numer. Anal. 46(2), 691-721 (2008)
    • (2008) SIAM J. Numer. Anal. , vol.46 , pp. 691-721
    • Blanchet, A.1    Calvez, V.2    Carrillo, J.A.3
  • 5
    • 10244229064 scopus 로고    scopus 로고
    • Precise computations of chemotactic collapse using moving mesh methods
    • DOI 10.1016/j.jcp.2004.07.010, PII S0021999104002943
    • Budd, C.J., Carretero-González, R., Russell, R.D.: Precise computations of chemotactic collapse using moving mesh methods. J. Comput. Phys. 202(2), 463-487 (2005) (Pubitemid 39620325)
    • (2005) Journal of Computational Physics , vol.202 , Issue.2 , pp. 463-487
    • Budd, C.J.1    Carretero-Gonzalez, R.2    Russell, R.D.3
  • 8
    • 33749243493 scopus 로고    scopus 로고
    • A finite volume scheme for the Patlak-Keller-Segel chemotaxis model
    • 4
    • Filbet, F.: A finite volume scheme for the Patlak-Keller-Segel chemotaxis model. Numer. Math. 104(4), 457-488 (2006)
    • (2006) Numer. Math. , vol.104 , pp. 457-488
    • Filbet, F.1
  • 9
    • 0003069987 scopus 로고
    • The numerical solution of the N-body problem
    • Greengard, L.: The numerical solution of the N-body problem. Comput. Phys. 4, 142-152 (1990)
    • (1990) Comput. Phys. , vol.4 , pp. 142-152
    • Greengard, L.1
  • 10
    • 67349252119 scopus 로고    scopus 로고
    • Stochastic particle approximation to the global measure valued solutions of the Keller-Segel model in 2D
    • to appear
    • Haskovec, J., Schmeiser, C.: Stochastic particle approximation to the global measure valued solutions of the Keller-Segel model in 2D. In: Proceedings of the Conference EQUADIFF 2007 (to appear)
    • Proceedings of the Conference EQUADIFF 2007
    • Haskovec, J.1    Schmeiser, C.2
  • 11
    • 0039712703 scopus 로고    scopus 로고
    • Singularity patterns in a chemotaxis model
    • Herrero, M.A., Velázquez, J.J.L.: Singularity patterns in a chemotaxis model. Math. Ann. 306, 583-623 (1996) (Pubitemid 126337673)
    • (1996) Mathematische Annalen , vol.306 , Issue.3 , pp. 583-623
    • Herrero, M.A.1    Velazquez, J.J.L.2
  • 12
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • Keller, E.F., Segel, L.A.: Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol. 26, 399-415 (1970)
    • (1970) J. Theor. Biol. , vol.26 , pp. 399-415
    • Keller, E.F.1    Segel, L.A.2
  • 13
    • 0344629886 scopus 로고    scopus 로고
    • 2D simulation of chemotactic bacteria aggregation
    • Marrocco, A.: 2D simulation of chemotactic bacteria aggregation. ESAIM: Math. Model. Numer. Anal. 37, 617-630 (2003)
    • (2003) ESAIM: Math. Model. Numer. Anal. , vol.37 , pp. 617-630
    • Marrocco, A.1
  • 14
    • 0000687738 scopus 로고    scopus 로고
    • Chemotactic collapse in a parabolic system of mathematical biology
    • 3
    • Nagai, T., Senba, T., Suzuki, T.: Chemotactic collapse in a parabolic system of mathematical biology. Hiroshima Math. J. 30(3), 463-497 (2000)
    • (2000) Hiroshima Math. J. , vol.30 , pp. 463-497
    • Nagai, T.1    Senba, T.2    Suzuki, T.3
  • 15
    • 84867975891 scopus 로고    scopus 로고
    • PDE models for chemotactic movements: Parabolic, hyperbolic and kinetic
    • Perthame, B.: PDE models for chemotactic movements: Parabolic, hyperbolic and kinetic. Appl. Math. 49 (2004)
    • (2004) Appl. Math. , vol.49
    • Perthame, B.1
  • 16
    • 18144399840 scopus 로고    scopus 로고
    • Diagonal Defect Measures, Adhesion Dynamics and Euler Equation
    • Poupaud, F.: Diagonal defect measures, adhesion dynamics and Euler equations. Methods Appl. Anal. 9, 533-561 (2002) (Pubitemid 37316796)
    • (2002) METHODS and APPLICATIONS of ANALYSIS , vol.9 , Issue.4 , pp. 533-562
    • Poupaud, F.1
  • 17
    • 34047151167 scopus 로고    scopus 로고
    • Conservative upwind finite element method for a simplified Keller-Segel system modelling chemotaxis
    • 2
    • Saito, N.: Conservative upwind finite element method for a simplified Keller-Segel system modelling chemotaxis. IMA J. Numer. Anal. 27(2), 332-365 (2007)
    • (2007) IMA J. Numer. Anal. , vol.27 , pp. 332-365
    • Saito, N.1
  • 18
    • 28444472731 scopus 로고    scopus 로고
    • Notes on finite difference schemes to a parabolic-elliptic system modelling chemotaxis
    • 1
    • Saito, N., Suzuki, T.: Notes on finite difference schemes to a parabolic-elliptic system modelling chemotaxis. Appl. Math. Comput. 171(1), 72-90 (2005)
    • (2005) Appl. Math. Comput. , vol.171 , pp. 72-90
    • Saito, N.1    Suzuki, T.2
  • 19
    • 4544331862 scopus 로고    scopus 로고
    • Point dynamics in a singular limit of the Keller-Segel model. (1) Motion of the concentration regions
    • 4
    • Velaázquez, J.J.L.: Point dynamics in a singular limit of the Keller-Segel model. (1) Motion of the concentration regions. SIAM J. Appl. Math. 64(4), 1198-1223 (2004)
    • (2004) SIAM J. Appl. Math. , vol.64 , pp. 1198-1223
    • Velaázquez, J.J.L.1
  • 20
    • 4544354402 scopus 로고    scopus 로고
    • Point dynamics in a singular limit of the Keller-Segel model. (2) Formation of the concentration regions
    • 4
    • Velaázquez, J.J.L.: Point dynamics in a singular limit of the Keller-Segel model. (2) Formation of the concentration regions. SIAM J. Appl. Math. 64(4), 1224-1248 (2004)
    • (2004) SIAM J. Appl. Math. , vol.64 , pp. 1224-1248
    • Velaázquez, J.J.L.1
  • 21
    • 4944255231 scopus 로고    scopus 로고
    • Well-posedness of a model of point dynamics for a limit of the Keller-Segel system
    • DOI 10.1016/j.jde.2004.05.013, PII S0022039604002062
    • Velázquez, J.J.L.: Well-posedness of a model of point dynamics for a limit of the Keller-Segel system. J. Differ. Equ. 206, 315-352 (2004) (Pubitemid 39332554)
    • (2004) Journal of Differential Equations , vol.206 , Issue.2 , pp. 315-352
    • Velazquez, J.J.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.