메뉴 건너뛰기




Volumn 65, Issue 1-2, 2009, Pages 79-102

On convergence to equilibria for a chemotaxis model with volume-filling effect

Author keywords

ojasiewicz Simon inequality; Chemotaxis model; Volume filling effect

Indexed keywords

ASYMPTOTIC BEHAVIOR OF SOLUTIONS; CHEMOTAXIS MODEL; DECAY RATE; NEUMANN BOUNDARY CONDITION; NON-SMOOTH; SIMON INEQUALITY;

EID: 72649106922     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: 10.3233/ASY-2009-0948     Document Type: Article
Times cited : (24)

References (30)
  • 1
    • 50849123026 scopus 로고    scopus 로고
    • A class of kinetic models for chemotaxis with threshold to prevent overcrowding
    • F.A.C.C. Chalub and J.F. Rodrigues, A class of kinetic models for chemotaxis with threshold to prevent overcrowding, Port. Math. 63(2) (2006), 227-250.
    • (2006) Port. Math. , vol.63 , Issue.2 , pp. 227-250
    • Chalub, F.A.C.C.1    Rodrigues, J.F.2
  • 2
    • 33750624355 scopus 로고    scopus 로고
    • Quasilinear nonuniformly parabolic system modelling chemotaxis
    • T. Ciéslak, Quasilinear nonuniformly parabolic system modelling chemotaxis, J. Math. Anal. Appl. 326 (2007), 1410-1426.
    • (2007) J. Math. Anal. Appl. , vol.326 , pp. 1410-1426
    • Ciéslak, T.1
  • 3
    • 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(1) (2005), 286-308.
    • (2005) SIAM J. Appl. Math. , vol.66 , Issue.1 , pp. 286-308
    • Dolak, Y.1    Schmeiser, C.2
  • 4
    • 1842843827 scopus 로고    scopus 로고
    • A non-smooth version of the Lojasiewicz-Simon theorem with applications to non-local phase-field systems
    • E. Feireisl, F. Issard-Roch and H. Petzeltová, A non-smooth version of the Lojasiewicz-Simon theorem with applications to non-local phase-field systems, J. Differential Equations 199 (2004), 1-21.
    • (2004) J. Differential Equations , vol.199 , pp. 1-21
    • Feireisl, E.1    Issard-Roch, F.2    Petzeltová, H.3
  • 5
    • 34247108617 scopus 로고    scopus 로고
    • On convergence to equilibria for the Keller-Segel chemotaxis model
    • E. Feireisl, Ph. Laurençot and H. Petzeltová, On convergence to equilibria for the Keller-Segel chemotaxis model, J. Differential Equations 236 (2007), 551-569.
    • (2007) J. Differential Equations , vol.236 , pp. 551-569
    • Feireisl, E.1    Laurençot, Ph.2    Petzeltová, H.3
  • 6
    • 0032445844 scopus 로고    scopus 로고
    • Global behaviour of a reaction-diffusion system modelling chemotaxis
    • H. Gajewski and K. Zacharias, Global behaviour 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
  • 7
    • 0142119425 scopus 로고    scopus 로고
    • On a nonlocal phase separation model
    • H. Gajewski and K. Zacharias, On a nonlocal phase separation model, J. Math. Anal. Appl. 286 (2003), 11-31.
    • (2003) J. Math. Anal. Appl. , vol.286 , pp. 11-31
    • Gajewski, H.1    Zacharias, K.2
  • 8
    • 84967780428 scopus 로고
    • Stability results for a diffusion equation with functional drift approximating a chemotaxis model
    • J.M. Greenberg and 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
  • 9
    • 0003304963 scopus 로고
    • Geometric theory of semilinear parabolic equations
    • Springer, Berlin
    • D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, Vol.840, Springer, Berlin, 1981.
    • (1981) Lecture Notes in Mathematics , vol.840
    • Henry, D.1
  • 10
    • 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 (2001), 280-301.
    • (2001) Adv. Appl. Math. , vol.26 , pp. 280-301
    • Hillen, T.1    Painter, K.2
  • 11
    • 4744373195 scopus 로고    scopus 로고
    • The one-dimensional chemotaxis model: Global existence and asymptotic profile
    • T. Hillen and A. Potapov, The one-dimensional chemotaxis model: Global existence and asymptotic profile, Math. Meth. Appl. Sci. 27 (2004), 1783-1801.
    • (2004) Math. Meth. Appl. Sci. , vol.27 , pp. 1783-1801
    • Hillen, T.1    Potapov, A.2
  • 12
    • 4744373150 scopus 로고
    • 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, Jahresber. Deutsch. Math.-Verein. 105 (2003), 103-165.
    • (1970) Jahresber. Deutsch. Math.-Verein. , vol.105 , pp. 103-165
    • Horstmann From, D.1
  • 13
    • 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, Jahresber. Deutsch. Math.-Verein. 106 (2004), 51-69.
    • (2004) Jahresber. Deutsch. Math.-Verein. , vol.106 , pp. 51-69
    • Horstmann, D.1
  • 14
    • 18144371222 scopus 로고    scopus 로고
    • Boundedness vs. blow-up in a chemotaxis system
    • D. Horstmann and M. Winkler, Boundedness vs. blow-up in a chemotaxis system, J. Differential Equations 215 (2005), 52-107.
    • (2005) J. Differential Equations , vol.215 , pp. 52-107
    • Horstmann, D.1    Winkler, M.2
  • 15
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • E. Keller and L. 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.1    Segel, L.2
  • 16
    • 44549087932 scopus 로고    scopus 로고
    • Local existence and finite time blow-up of solutions in the 2-D Keller-Segel system
    • H. Kozono and Y. Sugiyama, Local existence and finite time blow-up of solutions in the 2-D Keller-Segel system, J. Evol. Equ. 8 (2008), 353-378.
    • (2008) J. Evol. Equ. , vol.8 , pp. 353-378
    • Kozono, H.1    Sugiyama, Y.2
  • 17
    • 0000687738 scopus 로고    scopus 로고
    • Chemotactic collapse in a parabolic system of mathematical biology
    • T. Nagai, T. Senba and T. Suzuki, Chemotactic collapse in a parabolic system of mathematical biology, HiroshimaMath. J. 30 (2000), 463-497.
    • (2000) HiroshimaMath. J. , vol.30 , pp. 463-497
    • Nagai, T.1    Senba, T.2    Suzuki, T.3
  • 18
    • 0001205112 scopus 로고    scopus 로고
    • Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis
    • T. Nagai, T. Senba and K. Yoshida, Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis, Funkcial. Ekvac. 40 (1997), 411-433.
    • (1997) Funkcial. Ekvac. , vol.40 , pp. 411-433
    • Nagai, T.1    Senba, T.2    Yoshida, K.3
  • 19
    • 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, Can. Appl.Math. Q. 10 (2002), 501-543.
    • (2002) Can. Appl.Math. Q. , vol.10 , pp. 501-543
    • Painter, K.1    Hillen, T.2
  • 20
    • 51249193541 scopus 로고
    • Random walk with persistence and external bias
    • C.S. Patlak, Random walk with persistence and external bias, Bull. Math. Biophys. 15 (1953), 311-338.
    • (1953) Bull. Math. Biophys. , vol.15 , pp. 311-338
    • Patlak, C.S.1
  • 22
    • 0001373727 scopus 로고
    • Stationary solutions of chemotaxis systems
    • R. Schaaf, Stationary solutions of chemotaxis systems, Trans. Amer. Math. Soc. 292 (1985), 531-556.
    • (1985) Trans. Amer. Math. Soc. , vol.292 , pp. 531-556
    • Schaaf, R.1
  • 25
    • 34848920328 scopus 로고    scopus 로고
    • Classical solutions and pattern formation for a volume filling chemotaxis model
    • Z.Wang and T. Hillen, Classical solutions and pattern formation for a volume filling chemotaxis model, Chaos 17 (2007), 037108.
    • (2007) Chaos , vol.17 , pp. 037108
    • Wang, Z.1    Hillen, T.2
  • 26
    • 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 Anal. 59 (2004), 1293-1310.
    • (2004) Nonlinear Anal , vol.59 , pp. 1293-1310
    • Wrzosek, D.1
  • 27
    • 33646266962 scopus 로고    scopus 로고
    • Long-time behaviour of solutions to a chemotaxis model with volume-filling effect
    • D. Wrzosek, Long-time behaviour of solutions to a chemotaxis model with volume-filling effect, Proc. Roy. Soc. Edinburgh 136A (2006), 431-444.
    • (2006) Proc. Roy. Soc. Edinburgh , vol.136 A , pp. 431-444
    • Wrzosek, D.1
  • 29
    • 73849138636 scopus 로고    scopus 로고
    • The steady states and convergence to equilibria for a 1-D chemotaxis model with volume-filling effect
    • DOI:10.1002/mma.1147
    • Y. Zhang, The steady states and convergence to equilibria for a 1-D chemotaxis model with volume-filling effect, Math. Method. Appl. Sci., DOI: 10.1002/mma.1147.
    • Math. Method. Appl. Sci.
    • Zhang, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.