메뉴 건너뛰기




Volumn 17, Issue 3, 2007, Pages

Classical solutions and pattern formation for a volume filling chemotaxis model

Author keywords

[No Author keywords available]

Indexed keywords


EID: 34848920328     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2766864     Document Type: Article
Times cited : (117)

References (35)
  • 1
    • 0033531342 scopus 로고    scopus 로고
    • A minimum mechanism for bacterial pattern formation
    • R. Tyson, S. R. Lubin, and J. Murray, " A minimum mechanism for bacterial pattern formation., " Proc. R. Soc. London, Ser. B 266, 299-304 (1999).
    • (1999) Proc. R. Soc. London, Ser. B , vol.266 , pp. 299-304
    • Tyson, R.1    Lubin, S.R.2    Murray, J.3
  • 2
    • 0033112265 scopus 로고    scopus 로고
    • Models and analysis of chemotactic bacterial patterns in a liquid medium
    • R. Tyson, S. R. Lubin, and J. Murray, " Models and analysis of chemotactic bacterial patterns in a liquid medium., " J. Math. Biol. 38, 359-375 (1999).
    • (1999) J. Math. Biol. , vol.38 , pp. 359-375
    • Tyson, R.1    Lubin, S.R.2    Murray, J.3
  • 4
    • 0034792774 scopus 로고    scopus 로고
    • Amoeboid leuckocyte crawling through extracelluer matrix: Lessons from the Dictyostelium paradigm of cell movement
    • P. Friedl, S. Borgmann, and E. Bröcker, " Amoeboid leuckocyte crawling through extracelluer matrix: Lessons from the Dictyostelium paradigm of cell movement., " J. Leukoc Biol. 70, 491-509 (2001).
    • (2001) J. Leukoc Biol. , vol.70 , pp. 491-509
    • Friedl, P.1    Borgmann, S.2    Bröcker, E.3
  • 5
    • 0033545988 scopus 로고    scopus 로고
    • Stripe formation in juvenile Pomacanthus via chemotactic response to a reaction-diffusion mechanism
    • K. Painter, H. G. Othmer, and P. K. Maini, " Stripe formation in juvenile Pomacanthus via chemotactic response to a reaction-diffusion mechanism., " Proc. Natl. Acad. Sci. U.S.A. 96, 5549-5554 (1999).
    • (1999) Proc. Natl. Acad. Sci. U.S.A. , vol.96 , pp. 5549-5554
    • Painter, K.1    Othmer, H.G.2    Maini, P.K.3
  • 6
    • 0029294735 scopus 로고
    • Mathematical models for tumour angiogenesis-numerical simulations and nonlinear-wave equations
    • H. Byrne and M. Chaplain, " Mathematical models for tumour angiogenesis-numerical simulations and nonlinear-wave equations., " Bull. Math. Biol. 57, 461-485 (1995).
    • (1995) Bull. Math. Biol. , vol.57 , pp. 461-485
    • Byrne, H.1    Chaplain, M.2
  • 7
    • 0015011285 scopus 로고
    • Model for chemotaxis
    • E. Keller and L. Segel, " Model for chemotaxis., " J. Theor. Biol. 30, 225-234 (1971).
    • (1971) J. Theor. Biol. , vol.30 , pp. 225-234
    • Keller, E.1    Segel, L.2
  • 8
    • 4744373150 scopus 로고    scopus 로고
    • From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. i
    • D. Horstmann, " From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I., " Jahresberichte der Deutschen Mathematiker Vereinigung 105, 103-165 (2003).
    • (2003) Jahresberichte der Deutschen Mathematiker Vereinigung , vol.105 , pp. 103-165
    • Horstmann, D.1
  • 9
    • 13844288282 scopus 로고    scopus 로고
    • From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. II
    • D. Horstmann, " From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. II., " Jahresberichte der Deutschen Mathematiker Vereinigung 106, 51-69 (2004).
    • (2004) Jahresberichte der Deutschen Mathematiker Vereinigung , vol.106 , pp. 51-69
    • Horstmann, D.1
  • 10
    • 0030243891 scopus 로고    scopus 로고
    • Aggregating pattern dynamics in a chemotaxis model including growth
    • M. Mimura and T. Tsujikawa, " Aggregating pattern dynamics in a chemotaxis model including growth., " Physica D 230, 499-543 (1996).
    • (1996) Physica D , vol.230 , pp. 499-543
    • Mimura, M.1    Tsujikawa, T.2
  • 11
    • 0036778798 scopus 로고    scopus 로고
    • Exponential attractor for a chemotaxis-growth system of equations
    • K. Osaki, T. Tsujikawa, A. Yagi, and M. Mimura, " Exponential attractor for a chemotaxis-growth system of equations., " Nonlinear Analysis. 51, 119-144 (2002).
    • (2002) Nonlinear Analysis. , vol.51 , pp. 119-144
    • Osaki, K.1    Tsujikawa, T.2    Yagi, A.3    Mimura, M.4
  • 12
    • 0000657461 scopus 로고    scopus 로고
    • Local and global solvability of some parabolic systems modelling chemotaxis
    • P. Biler, " Local and global solvability of some parabolic systems modelling chemotaxis., " Adv. Math. Sci. Appl. 8, 715-743 (1998).
    • (1998) Adv. Math. Sci. Appl. , vol.8 , pp. 715-743
    • Biler, P.1
  • 13
    • 0032556650 scopus 로고    scopus 로고
    • Mathematical models for motile bacterial transport in cylindrical tubes
    • K. C. Chen, R. M. Ford, and P. T. Cummings, " Mathematical models for motile bacterial transport in cylindrical tubes., " J. Theor. Biol. 195, 481-504 (1998).
    • (1998) J. Theor. Biol. , vol.195 , pp. 481-504
    • Chen, K.C.1    Ford, R.M.2    Cummings, P.T.3
  • 14
    • 0031207030 scopus 로고    scopus 로고
    • Aggregation, blowup and collapse: The ABC'c of taxis in reinforced random walks
    • H. G. Othmer and A. Stevens, " Aggregation, blowup and collapse: The ABC'c of taxis in reinforced random walks., " SIAM J. Appl. Math. 57, 1044-1081 (1997).
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1044-1081
    • Othmer, H.G.1    Stevens, A.2
  • 16
    • 0038645352 scopus 로고    scopus 로고
    • Chemotactic signaling, microglia, and Alzheimer's disease senile plaques: Is there a connection?
    • M. Luca, A. Chaves-Ross, L. Edelstein-Keshet, and A. Mogilner, " Chemotactic signaling, microglia, and Alzheimer's disease senile plaques: Is there a connection? " Bull. Math. Biol. 65, 693-730 (2003).
    • (2003) Bull. Math. Biol. , vol.65 , pp. 693-730
    • Luca, M.1    Chaves-Ross, A.2    Edelstein-Keshet, L.3    Mogilner, A.4
  • 17
    • 4944248574 scopus 로고    scopus 로고
    • Volume-filling and quorum-sensing in models for chemosensitive movement
    • K. Painter and T. Hillen, " Volume-filling and quorum-sensing in models for chemosensitive movement., " Canadian Applied Mathematics Quarterly. 10, 501-543 (2002).
    • (2002) Canadian Applied Mathematics Quarterly. , vol.10 , pp. 501-543
    • Painter, K.1    Hillen, T.2
  • 18
    • 0034304765 scopus 로고    scopus 로고
    • Complex spatial patterns in a hybrid chemotaxis reaction-diffusion model
    • K. Painter, P. K. Maini, and H. G. Othmer, " Complex spatial patterns in a hybrid chemotaxis reaction-diffusion model., " J. Math. Biol. 41, 285-314 (2000).
    • (2000) J. Math. Biol. , vol.41 , pp. 285-314
    • Painter, K.1    Maini, P.K.2    Othmer, H.G.3
  • 21
    • 36549091346 scopus 로고
    • Surface exclusion effects in adsorption processes
    • R. Schaaf and J. Talbot, " Surface exclusion effects in adsorption processes., " J. Chem. Phys. 91, 4401-4409 (1989).
    • (1989) J. Chem. Phys. , vol.91 , pp. 4401-4409
    • Schaaf, R.1    Talbot, J.2
  • 22
    • 21244493212 scopus 로고    scopus 로고
    • Metastability in chemotaxis models
    • A. Potapov and T. Hillen, " Metastability in chemotaxis models., " J. Dyn. Differ. Equ. 17, 293-330 (2005).
    • (2005) J. Dyn. Differ. Equ. , vol.17 , pp. 293-330
    • Potapov, A.1    Hillen, T.2
  • 24
    • 0001404830 scopus 로고    scopus 로고
    • Global existence for a parabolic chemotaxis model with prevention of overcrowding
    • T. Hillen and K. Painter, " Global existence for a parabolic chemotaxis model with prevention of overcrowding., " Adv. Appl. Math. 26, 280-301 (2001).
    • (2001) Adv. Appl. Math. , vol.26 , pp. 280-301
    • Hillen, T.1    Painter, K.2
  • 25
    • 9244236567 scopus 로고    scopus 로고
    • Global attractor for a chemotaxis model with prevention of overcrowding
    • D. Wrzosek, " Global attractor for a chemotaxis model with prevention of overcrowding., " Nonlinear Analysis. 59, 1293-1310 (2004).
    • (2004) Nonlinear Analysis. , vol.59 , pp. 1293-1310
    • Wrzosek, D.1
  • 26
    • 84972541997 scopus 로고
    • Dynamic theory of quasilinear parabolic equations II: Reation-diffusion systems
    • H. Amann, " Dynamic theory of quasilinear parabolic equations II: Reation-diffusion systems., " Diff. Integral Eq. 3, 13-75 (1990).
    • (1990) Diff. Integral Eq. , vol.3 , pp. 13-75
    • Amann, H.1
  • 27
    • 0001742516 scopus 로고
    • Dynamic theory of quasilinear parabolic equations III: Global existence
    • H. Amann, " Dynamic theory of quasilinear parabolic equations III: Global existence., " Math. Z. 202, 219-250 (1989).
    • (1989) Math. Z. , vol.202 , pp. 219-250
    • Amann, H.1
  • 28
    • 0001835099 scopus 로고
    • Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems
    • Function Spaces, edited by H. J.Schmeisser, H.Triebel (Teubner, Stuttgart
    • H. Amann, " Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems., " in Function Spaces, Differential Operators and Nonlinear Analysis, edited by, H. J. Schmeisser, H. Triebel, (Teubner, Stuttgart, 1993), pp. 9-126.
    • (1993) Differential Operators and Nonlinear Analysis , pp. 9-126
    • Amann, H.1
  • 29
    • 0005525774 scopus 로고    scopus 로고
    • Lyapunov functions and Lp estimates for a class of reaction-diffusion systems
    • D. Horstmann, " Lyapunov functions and Lp estimates for a class of reaction-diffusion systems., " Colloq. Math. 87, 113-127 (2001).
    • (2001) Colloq. Math. , vol.87 , pp. 113-127
    • Horstmann, D.1
  • 32
    • 33644610345 scopus 로고    scopus 로고
    • The Keller-Segel model with logistic sensitivity function and small diffusivity
    • Y. Dolak and C. Schmeiser, " The Keller-Segel model with logistic sensitivity function and small diffusivity., " SIAM J. Appl. Math. 66, 286-308 (2005).
    • (2005) SIAM J. Appl. Math. , vol.66 , pp. 286-308
    • Dolak, Y.1    Schmeiser, C.2
  • 33
    • 31144461544 scopus 로고    scopus 로고
    • Mesa-type patterns in the one-dimensional Brusselator and their stability
    • T. Kolokolnikov, T. Erneux, and J. Wei, " Mesa-type patterns in the one-dimensional Brusselator and their stability., " Physica D 214, 63-77 (2006).
    • (2006) Physica D , vol.214 , pp. 63-77
    • Kolokolnikov, T.1    Erneux, T.2    Wei, J.3
  • 34
    • 34248370060 scopus 로고    scopus 로고
    • The Keller-Segel model for chemotaxis with prevention of overcrowding: Linear and nonlinear diffusion
    • M. Burger, M. Francesco, and Y. Dolak, " The Keller-Segel model for chemotaxis with prevention of overcrowding: Linear and nonlinear diffusion., " SIAM J. Math. Anal. 38, 1288-1315 (2006).
    • (2006) SIAM J. Math. Anal. , vol.38 , pp. 1288-1315
    • Burger, M.1    Francesco, M.2    Dolak, Y.3
  • 35
    • 33646266962 scopus 로고    scopus 로고
    • Long time behavior of solutions to a chemotaxis model with volume filling effects
    • D. Wrzosek, " Long time behavior of solutions to a chemotaxis model with volume filling effects., " Proc. - R. Soc. Edinburgh, Sect. A: Math. 136, 431-444 (2006).
    • (2006) Proc. - R. Soc. Edinburgh, Sect. A: Math. , vol.136 , pp. 431-444
    • Wrzosek, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.