메뉴 건너뛰기




Volumn 1, Issue 3, 2000, Pages 409-433

Hyperbolic models for chemotaxis in 1-D

Author keywords

Chemotaxis; Correlated random walks; Hyperbolic equations; Parabolic limit

Indexed keywords


EID: 0034259466     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(99)00284-9     Document Type: Article
Times cited : (76)

References (50)
  • 1
    • 0019188958 scopus 로고
    • Biased random walk model for chemotaxis and related diffusion approximation
    • W. Alt, Biased random walk model for chemotaxis and related diffusion approximation, J. Math. Biol. 9 (1980) 147-177.
    • (1980) J. Math. Biol. , vol.9 , pp. 147-177
    • Alt, W.1
  • 2
    • 0003135551 scopus 로고
    • Singular perturbation of differential integral equations describing biased random walks
    • W. Alt, Singular perturbation of differential integral equations describing biased random walks, J. Für die Reine und Angewandte Mathematik 322 (1981) 15-41.
    • (1981) J. Für die Reine und Angewandte Mathematik , vol.322 , pp. 15-41
    • Alt, W.1
  • 3
    • 0016180376 scopus 로고
    • Chemotaxis in Escherichia coli analyzed by three-dimensional tracing
    • H.C. Berg, D.A. Brown, Chemotaxis in Escherichia coli analyzed by three-dimensional tracing, Antibiotics and Chemotherapy 19 (1974) 55-78.
    • (1974) Antibiotics and Chemotherapy , vol.19 , pp. 55-78
    • Berg, H.C.1    Brown, D.A.2
  • 4
    • 0000111586 scopus 로고
    • Growth and accretion of mass in an astrophysical model
    • P. Biler, Growth and accretion of mass in an astrophysical model, Appl. Math. 23 (2) (1995) 179-189.
    • (1995) Appl. Math. , vol.23 , Issue.2 , pp. 179-189
    • Biler, P.1
  • 5
    • 0001247718 scopus 로고
    • Growth and accretion of mass in an astrophysical model II
    • P. Biler, T. Nadzieja, Growth and accretion of mass in an astrophysical model II, Appl. Math. 23 (3) (1995) 351-361.
    • (1995) Appl. Math. , vol.23 , Issue.3 , pp. 351-361
    • Biler, P.1    Nadzieja, T.2
  • 7
    • 0032153759 scopus 로고    scopus 로고
    • Perturbation expansion of Alt's cell balance equations reduces to Segel's one-dimensional equation for shallow chemoattractant gradients
    • K.C. Chen, R.M. Ford, P.T. Cummings, Perturbation expansion of Alt's cell balance equations reduces to Segel's one-dimensional equation for shallow chemoattractant gradients, SIAM J. Appl. Math. 59 (1) (1999) 35-57.
    • (1999) SIAM J. Appl. Math. , vol.59 , Issue.1 , pp. 35-57
    • Chen, K.C.1    Ford, R.M.2    Cummings, P.T.3
  • 8
    • 0002166459 scopus 로고
    • Chemotactic collapse in two dimensions
    • S. Childress, Chemotactic collapse in two dimensions, Lect. Notes Biomath. 55 (1984) 61-68.
    • (1984) Lect. Notes Biomath. , vol.55 , pp. 61-68
    • Childress, S.1
  • 9
    • 0019784884 scopus 로고
    • Nonlinear aspects of chemotaxis
    • S. Childress, J.K. Percus, Nonlinear aspects of chemotaxis, Math. Biosci. 56 (1981) 217-237.
    • (1981) Math. Biosci. , vol.56 , pp. 217-237
    • Childress, S.1    Percus, J.K.2
  • 11
    • 0026932947 scopus 로고
    • On the relationship between cell balance equations for chemotactic cell populations
    • R.M. Ford, P.T. Cummings, On the relationship between cell balance equations for chemotactic cell populations, SIAM Appl. Math. 52 (1992) 1426-1441.
    • (1992) SIAM Appl. Math. , vol.52 , pp. 1426-1441
    • Ford, R.M.1    Cummings, P.T.2
  • 12
    • 0002117388 scopus 로고
    • Errata to: On the relationship between cell balance equations for chemotactic cell populations
    • R.M. Ford, P.T. Cummings, Errata to: On the relationship between cell balance equations for chemotactic cell populations, SIAM J. Appl. Math. 53 (1993) 1505.
    • (1993) SIAM J. Appl. Math. , vol.53 , pp. 1505
    • Ford, R.M.1    Cummings, P.T.2
  • 13
    • 0032445844 scopus 로고    scopus 로고
    • Global behavior of a reaction-diffusion system modelling chemotaxis
    • H. Gajewski, K. Zacharias, Global behavior of a reaction-diffusion system modelling chemotaxis, Math. Nachr. 195 (1998) 77-114.
    • (1998) Math. Nachr. , vol.195 , pp. 77-114
    • Gajewski, H.1    Zacharias, K.2
  • 15
    • 0001229778 scopus 로고
    • On diffusion by discontinuous movements and the telegraph equation
    • S. Goldstein, On diffusion by discontinuous movements and the telegraph equation, Quart. J. Mech. Appl. Math. 4 (1951) 129-156.
    • (1951) Quart. J. Mech. Appl. Math. , vol.4 , pp. 129-156
    • Goldstein, S.1
  • 16
    • 84967780428 scopus 로고
    • Stability results for a diffusion equation with functional drift approximating a chemotaxis model
    • J.M. Greenberg, W. Alt, Stability results for a diffusion equation with functional drift approximating a chemotaxis model, Trans. Amer. Math. Soc. 300 (1) (1987) 235-258.
    • (1987) Trans. Amer. Math. Soc. , vol.300 , Issue.1 , pp. 235-258
    • Greenberg, J.M.1    Alt, W.2
  • 17
    • 0002395653 scopus 로고
    • Travelling fronts for correlated random walks
    • K.P. Hadeler, Travelling fronts for correlated random walks, Canad. Appl. Math. Quart. 2 (1994) 27-43.
    • (1994) Canad. Appl. Math. Quart. , vol.2 , pp. 27-43
    • Hadeler, K.P.1
  • 18
    • 0002324855 scopus 로고    scopus 로고
    • Reaction telegraph equations and random walk systems
    • (S. Von Strien, S. Verduyn Lunel, eds.), Roy. Acad. of the Netherlands. North Holland, Amsterdam
    • K.P. Hadeler, Reaction telegraph equations and random walk systems, in: Stochastic and Spatial Structures of Dynamical Systems (S. Von Strien, S. Verduyn Lunel, eds.), Roy. Acad. of the Netherlands. North Holland, Amsterdam (1996) 133-161.
    • (1996) Stochastic and Spatial Structures of Dynamical Systems , pp. 133-161
    • Hadeler, K.P.1
  • 19
    • 0000674134 scopus 로고
    • Travelling fronts in random walk systems
    • K.P. Hadeler, Travelling fronts in random walk systems, FORMA Japan 10 (3) (1995) 223-233.
    • (1995) FORMA Japan , vol.10 , Issue.3 , pp. 223-233
    • Hadeler, K.P.1
  • 20
    • 0030334089 scopus 로고    scopus 로고
    • Chemotactic collapse for the Keller-Segel model
    • M. Herrero, J. Velázquez, Chemotactic collapse for the Keller-Segel model, J. Math. Biol. 35 (2) (1996) 177-194.
    • (1996) J. Math. Biol. , vol.35 , Issue.2 , pp. 177-194
    • Herrero, M.1    Velázquez, J.2
  • 21
    • 0039712703 scopus 로고    scopus 로고
    • Singularity patterns in a chemotaxis model
    • M. Herrero, J. Velázquez, Singularity patterns in a chemotaxis model, Math. Annalen 306 (1996) 583-623.
    • (1996) Math. Annalen , vol.306 , pp. 583-623
    • Herrero, M.1    Velázquez, J.2
  • 24
    • 0002164275 scopus 로고    scopus 로고
    • Qualitative analysis of hyperbolic random walk systems
    • T. Hillen, Qualitative analysis of hyperbolic random walk systems, SFB 382, Report No. 43, 1996.
    • (1996) SFB 382, Report , vol.43
    • Hillen, T.1
  • 25
    • 0002458189 scopus 로고    scopus 로고
    • A Turing model with correlated random walk
    • T. Hillen, A Turing model with correlated random walk, J. Math. Biol. 35 (1996) 49-72.
    • (1996) J. Math. Biol. , vol.35 , pp. 49-72
    • Hillen, T.1
  • 26
    • 0031150104 scopus 로고    scopus 로고
    • Invariance principles for hyperbolic random walk systems
    • T. Hillen, Invariance principles for hyperbolic random walk systems, J. Math. Anal. Appl. 210 (1997) 360-374.
    • (1997) J. Math. Anal. Appl. , vol.210 , pp. 360-374
    • Hillen, T.1
  • 27
    • 85037803204 scopus 로고    scopus 로고
    • Existence of weak solutions for a hyperbolic chemotaxis model
    • submitted for publication
    • T. Hillen, C. Rohde, Existence of weak solutions for a hyperbolic chemotaxis model, J. Math. Anal. Appl. 1999, submitted for publication.
    • (1999) J. Math. Anal. Appl.
    • Hillen, T.1    Rohde, C.2
  • 28
    • 0027333299 scopus 로고
    • Are diffusion models too simple? A comparison with telegraph models of invasion
    • E.E. Holmes, Are diffusion models too simple? A comparison with telegraph models of invasion, Amer. Naturalist 142 (1993) 779-795.
    • (1993) Amer. Naturalist , vol.142 , pp. 779-795
    • Holmes, E.E.1
  • 29
    • 84966208077 scopus 로고
    • On explosions of solutions to a system of partial differential equations modelling chemotaxis
    • W. Jäger, S. Luckhaus, On explosions of solutions to a system of partial differential equations modelling chemotaxis, Trans. Amer. Math. Soc. 329 (1992) 819-824.
    • (1992) Trans. Amer. Math. Soc. , vol.329 , pp. 819-824
    • Jäger, W.1    Luckhaus, S.2
  • 30
    • 84858771454 scopus 로고
    • A stochastic model related to the telegrapher's equation
    • M. Kac, A stochastic model related to the telegrapher's equation, Rocky Mountain J. Math. 4 (1974) 497-509.
    • (1974) Rocky Mountain J. Math. , vol.4 , pp. 497-509
    • Kac, M.1
  • 31
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • E.F. Keller, L.A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theoret. Biol. 26 (1970) 399-415.
    • (1970) J. Theoret. Biol. , vol.26 , pp. 399-415
    • Keller, E.F.1    Segel, L.A.2
  • 33
    • 0031162898 scopus 로고    scopus 로고
    • A system of reaction diffusion equations arising in the theory of reinforced random walks
    • H.A. Levine, B.D. Sleeman, A system of reaction diffusion equations arising in the theory of reinforced random walks, SIAM J. Appl. Math. 57 (1997) 683-730.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 683-730
    • Levine, H.A.1    Sleeman, B.D.2
  • 34
    • 0032163453 scopus 로고    scopus 로고
    • Modulation equations and parabolic limits of reaction random walk systems
    • J. Müller, T. Hillen, Modulation equations and parabolic limits of reaction random walk systems, Math. Methods Appl. Sci. 21 (1998) 1207-1226.
    • (1998) Math. Methods Appl. Sci. , vol.21 , pp. 1207-1226
    • Müller, J.1    Hillen, T.2
  • 36
    • 0000911252 scopus 로고
    • Blow up of radially symmetric solutions to a chemotaxis system
    • T. Nagai, Blow up of radially symmetric solutions to a chemotaxis system, Adv. Math. Sci. Appl. 5 (1995) 581-601.
    • (1995) Adv. Math. Sci. Appl. , vol.5 , pp. 581-601
    • Nagai, T.1
  • 37
    • 0023746235 scopus 로고
    • Models of dispersal in biological systems
    • H.G. Othmer, S.R. Dunbar, W. Alt, Models of dispersal in biological systems, J. Math. Biol. 26 (1988) 263-298.
    • (1988) J. Math. Biol. , vol.26 , pp. 263-298
    • Othmer, H.G.1    Dunbar, S.R.2    Alt, W.3
  • 38
    • 0000711026 scopus 로고    scopus 로고
    • Oscillatory cAMP signaling in the development of Dictyostelium discoideum
    • H.G. Othmer, P. Schaap, Oscillatory cAMP signaling in the development of Dictyostelium discoideum, Comments Theoret. Biol. 5 (1998) 175-282.
    • (1998) Comments Theoret. Biol. , vol.5 , pp. 175-282
    • Othmer, H.G.1    Schaap, P.2
  • 39
    • 0031207030 scopus 로고    scopus 로고
    • Aggregation, blowup and collapse: The ABC's of taxis in reinforced random walks
    • H.G. Othmer, A. Stevens, Aggregation, blowup and collapse: The ABC's of taxis in reinforced random walks, SIAM J. Appl. Math. 57 (1997) 1044-1081.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1044-1081
    • Othmer, H.G.1    Stevens, A.2
  • 41
    • 0344750002 scopus 로고
    • A one dimensional model for the swarming behavior of myxobacteria
    • in: W. Alt, G. Hoffmann (Eds.), Springer, Berlin
    • B. Pfistner, A one dimensional model for the swarming behavior of myxobacteria, in: W. Alt, G. Hoffmann (Eds.), Biological Motion, Lect. Notes on Biomath., Vol. 89, Springer, Berlin, 1990.
    • (1990) Biological Motion, Lect. Notes on Biomath. , vol.89
    • Pfistner, B.1
  • 42
    • 0024940626 scopus 로고
    • Transport models for chemotactic cell populations based on individual cell behavior
    • M.A. Rivero, R.T. Tranquillo, H.M. Buettner, D.A. Lauffenburger, Transport models for chemotactic cell populations based on individual cell behavior, Chem. Eng. Sci. 44 (1989) 1-17.
    • (1989) Chem. Eng. Sci. , vol.44 , pp. 1-17
    • Rivero, M.A.1    Tranquillo, R.T.2    Buettner, H.M.3    Lauffenburger, D.A.4
  • 43
    • 0001595172 scopus 로고
    • A theoretical study of receptor mechanisms in bacterial chemotaxis
    • L.A. Segel, A theoretical study of receptor mechanisms in bacterial chemotaxis, SIAM Appl. Math. 32 (1977) 653-665.
    • (1977) SIAM Appl. Math. , vol.32 , pp. 653-665
    • Segel, L.A.1
  • 44
    • 0001928261 scopus 로고    scopus 로고
    • Blow-up of radially symmetric solutions to some systems of partial differential equations modelling chemotaxis
    • T. Senba, Blow-up of radially symmetric solutions to some systems of partial differential equations modelling chemotaxis, Adv. Math. Sci. Appl. 7 (1997) 79-92.
    • (1997) Adv. Math. Sci. Appl. , vol.7 , pp. 79-92
    • Senba, T.1
  • 45
    • 0000802743 scopus 로고
    • Behavioral studies into the mechanism of eukaryotic chemotaxis
    • D.R. Soll, Behavioral studies into the mechanism of eukaryotic chemotaxis, J. Chem. Ecol. 16 (1990) 133-150.
    • (1990) J. Chem. Ecol. , vol.16 , pp. 133-150
    • Soll, D.R.1
  • 46
    • 0000389227 scopus 로고
    • A model for gliding and aggregation of myxobacteria
    • in: M. Markus, A. Holden, H.G. Othmer (Eds.), Plenum Press, New York
    • A. Stevens, A model for gliding and aggregation of myxobacteria, in: M. Markus, A. Holden, H.G. Othmer (Eds.), Proceeding of Conference on Nonlinear Wave Processes in Excitable Media, Plenum Press, New York, 1991, pp. 269-276.
    • (1991) Proceeding of Conference on Nonlinear Wave Processes in Excitable Media , pp. 269-276
    • Stevens, A.1
  • 47
    • 85037797776 scopus 로고    scopus 로고
    • Derivation of chemotaxis-equations as limit dynamics of moderately interacting stochastic many particle systems
    • to appear
    • A. Stevens, Derivation of chemotaxis-equations as limit dynamics of moderately interacting stochastic many particle systems, SIAM J. Appl. Math. (1999), to appear.
    • (1999) SIAM J. Appl. Math.
    • Stevens, A.1
  • 48
    • 85037803672 scopus 로고    scopus 로고
    • A stochastic cellular automaton, modeling gliding and aggregation of myxobacteria
    • to appear
    • A. Stevens, A stochastic cellular automaton, modeling gliding and aggregation of myxobacteria, SIAM J. Appl. Math. (1999), to appear.
    • (1999) SIAM J. Appl. Math.
    • Stevens, A.1
  • 49
    • 0000843306 scopus 로고
    • Some stochastic processes which arise from a model of the motion of a bacterium
    • D.W. Stroock, Some stochastic processes which arise from a model of the motion of a bacterium, Probab. Theory Related Fields 28 (1974) 305-315.
    • (1974) Probab. Theory Related Fields , vol.28 , pp. 305-315
    • Stroock, D.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.