메뉴 건너뛰기




Volumn 184, Issue 2, 2002, Pages 386-421

Self-similar solutions to a parabolic system modeling chemotaxis

Author keywords

Blow up analysis; Chemotaxis; Parabolic system; Radial symmetry; Self similar solution

Indexed keywords


EID: 0037144962     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2001.4146     Document Type: Article
Times cited : (29)

References (36)
  • 1
    • 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 (1998), 715-743.
    • (1998) Adv. Math. Sci. Appl , vol.8 , pp. 715-743
    • Biler, P.1
  • 3
    • 0010915690 scopus 로고    scopus 로고
    • 2u in dimension two
    • 2u in dimension two, Comm. Anal. Geom. 7 (1999), 295-302.
    • (1999) Comm. Anal. Geom , vol.7 , pp. 295-302
    • Chen, X.1
  • 4
    • 0002166459 scopus 로고
    • "Chemotactic Collapse in Two Dimensions"
    • Springer, Berlin
    • S. Childress, "Chemotactic Collapse in Two Dimensions," Lecture Notes in Biomathematics, Vol. 55, pp. 217-237, Springer, Berlin, 1984.
    • (1984) Lecture Notes in Biomathematics , vol.55 , pp. 217-237
    • Childress, S.1
  • 5
    • 0019784884 scopus 로고
    • Nonlinear aspects of chemotaxis
    • S. Childress and 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
  • 6
    • 0000457881 scopus 로고
    • Variational problems related to self-similar solutions for the heat equation
    • M. Escobedo and O. Kavian, Variational problems related to self-similar solutions for the heat equation, Nonlinear Anal. TMA 11 (1987), 1103-1133.
    • (1987) Nonlinear Anal. TMA , vol.11 , pp. 1103-1133
    • Escobedo, M.1    Kavian, O.2
  • 7
    • 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
  • 8
    • 34250271532 scopus 로고
    • Symmetry and related properties via the maximum principle
    • B. Gidas, W.-M. Ni, and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209-243.
    • (1979) Comm. Math. Phys , vol.68 , pp. 209-243
    • Gidas, B.1    Ni, W.-M.2    Nirenberg, L.3
  • 9
    • 0000924617 scopus 로고
    • n
    • "Mathematical Analysis and Applications Part A" (L. Nachbin, Ed.), Academic Press, New York
    • n, in "Mathematical Analysis and Applications, Part A" (L. Nachbin, Ed.), Advances in Mathematics Supplementary Studies, Vol. 7, pp. 369-402, Academic Press, New York, 1981.
    • (1981) Advances in Mathematics Supplementary Studies , vol.7 , pp. 369-402
    • Gidas, B.1    Ni, W.-M.2    Nirenberg, L.3
  • 10
    • 0001226214 scopus 로고
    • Large time behavior of the vorticity of two-dimensional viscous flow and its application to vortex formation
    • Y. Giga and T. Kambe, Large time behavior of the vorticity of two-dimensional viscous flow and its application to vortex formation, Comm. Math. Phys. 117 (1988), 549-568.
    • (1988) Comm. Math. Phys , vol.117 , pp. 549-568
    • Giga, Y.1    Kambe, T.2
  • 11
    • 0003549965 scopus 로고
    • "Elliptic Partial Differential Equations of the Second Order"
    • Springer-Verlag, Berlin
    • D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of the Second Order," Springer-Verlag, Berlin, 1983.
    • (1983)
    • Gilbarg, D.1    Trudinger, N.S.2
  • 12
    • 0010853645 scopus 로고    scopus 로고
    • Concentration lemma, Brezis-Merle type inequality, and a parabolic system of chemotaxis
    • G. Harada, T. Nagai, T. Senba, and T. Suzuki, Concentration lemma, Brezis-Merle type inequality, and a parabolic system of chemotaxis, Adv. Differential Equations 6 (2001), 1255-1280.
    • (2001) Adv. Differential Equations , vol.6 , pp. 1255-1280
    • Harada, G.1    Nagai, T.2    Senba, T.3    Suzuki, T.4
  • 14
    • 0039712703 scopus 로고    scopus 로고
    • Singularity patterns in a chemotaxis model
    • M. A. Herrero and J. J. L. Velázquez, Singularity patterns in a chemotaxis model, Math. Ann. 306 (1996), 583-623.
    • (1996) Math. Ann , vol.306 , pp. 583-623
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 15
    • 0030334089 scopus 로고    scopus 로고
    • Chemotactic collapse for the Keller-Segel model
    • M. A. Herrero and J. J. L. Velázquez, Chemotactic collapse for the Keller-Segel model, J. Math. Biol. 35 (1996), 177-196.
    • (1996) J. Math. Biol , vol.35 , pp. 177-196
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 17
    • 0035646454 scopus 로고    scopus 로고
    • Blow-up in a chemotaxis model without symmetry assumptions
    • D. Horstmann and G. Wang, Blow-up in a chemotaxis model without symmetry assumptions, European J. Appl. Math. 12 (2001), 159-177.
    • (2001) European J. Appl. Math , vol.12 , pp. 159-177
    • Horstmann, D.1    Wang, G.2
  • 18
    • 84966208077 scopus 로고
    • On explosions of solutions to a system of partial differential equations modelling chemotaxis
    • W. Jäger, and 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
  • 19
    • 84948486085 scopus 로고
    • Remarks on the large time behavior of a nonlinear diffusion equation
    • O. Kavian, Remarks on the large time behavior of a nonlinear diffusion equation, Ann. Inst. H. Poincaré-Anal. Nonlinéaire 4 (1987), 423-452.
    • (1987) Ann. Inst. H. Poincaré-Anal. Nonlinéaire , vol.4 , pp. 423-452
    • Kavian, O.1
  • 20
    • 0030363289 scopus 로고    scopus 로고
    • Asymptotic behavior of solutions of a semilinear heat equation with subcritical nonlinearity
    • T. Kawanago, Asymptotic behavior of solutions of a semilinear heat equation with subcritical nonlinearity, Ann. Inst. H. Poincaré-Anal. Nonlinéaire 13 (1996), 1-15.
    • (1996) Ann. Inst. H. Poincaré-Anal. Nonlinéaire , vol.13 , pp. 1-15
    • Kawanago, T.1
  • 21
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • E. F. Keller and L. A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol. 26 (1970), 399-415.
    • (1970) J. Theor. Biol , vol.26 , pp. 399-415
    • Keller, E.F.1    Segel, L.A.2
  • 22
    • 0033248355 scopus 로고    scopus 로고
    • Harnack type inequality: The method of moving planes
    • Y-.Y. Li, Harnack type inequality: the method of moving planes, Comm. Math. Phys. 200 (1999), 421-444.
    • (1999) Comm. Math. Phys , vol.200 , pp. 421-444
    • Li, Y.-Y.1
  • 24
    • 0001543844 scopus 로고
    • The exterior Dirichlet problem for second order elliptic partial differential equations
    • N. Meyers and J. Serrin, The exterior Dirichlet problem for second order elliptic partial differential equations, J. Math. Mech. 9 (1960), 513-538.
    • (1960) J. Math. Mech , vol.9 , pp. 513-538
    • Meyers, N.1    Serrin, J.2
  • 25
    • 0000719354 scopus 로고    scopus 로고
    • Self-similar radial solutions to a parabolic system modelling chemotaxis via variational method
    • Y. Mizutani, N. Muramoto, and K. Yoshida, Self-similar radial solutions to a parabolic system modelling chemotaxis via variational method, Hiroshima Math. J. 29 (1999), 145-160.
    • (1999) Hiroshima Math. J , vol.29 , pp. 145-160
    • Mizutani, Y.1    Muramoto, N.2    Yoshida, K.3
  • 26
    • 0001932520 scopus 로고
    • Self-similar radial solutions to a system of partial differential equations modelling chemotaxis
    • Y. Mizutani and T. Nagai, Self-similar radial solutions to a system of partial differential equations modelling chemotaxis, Bull. Kyushu Inst. Tech. Math. Natur. Sci. 42 (1995), 19-28.
    • (1995) Bull. Kyushu Inst. Tech. Math. Natur. Sci , vol.42 , pp. 19-28
    • Mizutani, Y.1    Nagai, T.2
  • 27
    • 0010784598 scopus 로고    scopus 로고
    • Existence of self-similar solutions to a parabolic system modelling chemotaxis
    • N. Muramoto, Y. Naito, and K. Yoshida, Existence of self-similar solutions to a parabolic system modelling chemotaxis, Jpn. J. Ind. Appl. Math. 17 (2000), 427-451.
    • (2000) Jpn. J. Ind. Appl. Math , vol.17 , pp. 427-451
    • Muramoto, N.1    Naito, Y.2    Yoshida, K.3
  • 28
    • 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
  • 29
    • 0010786688 scopus 로고    scopus 로고
    • Blow-up of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domain
    • T. Nagai, Blow-up of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domain, J. Inequality Appl. 6 (2001), 37-55.
    • (2001) J. Inequality Appl , vol.6 , pp. 37-55
    • Nagai, T.1
  • 30
    • 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
  • 31
    • 0010852697 scopus 로고    scopus 로고
    • Radial symmetry of self-similar solutions for semilinear heat equations
    • Y. Naito and T. Suzuki, Radial symmetry of self-similar solutions for semilinear heat equations, J. Differential Equations 163 (2000), 407-428.
    • (2000) J. Differential Equations , vol.163 , pp. 407-428
    • Naito, Y.1    Suzuki, T.2
  • 32
    • 0015757937 scopus 로고
    • Chemotaxis, signal relaying, and aggregation morphology
    • V. Nanjundiah, Chemotaxis, signal relaying, and aggregation morphology, J. Theor. Biol. 42 (1973), 173-105.
    • (1973) J. Theor. Biol , vol.42 , pp. 173-105
    • Nanjundiah, V.1
  • 33
    • 0004014565 scopus 로고
    • "Maximum Principles in Differential Equations"
    • Prentice-Hall, Englewood Cliffs, NJ
    • M. Protter and H. Weinberger, "Maximum Principles in Differential Equations," Prentice-Hall, Englewood Cliffs, NJ, 1967.
    • (1967)
    • Protter, M.1    Weinberger, H.2
  • 34
    • 0002819277 scopus 로고    scopus 로고
    • Chemotactic collapse in a parabolic-elliptic system of mathematical biology
    • T. Senba and T. Suzuki, Chemotactic collapse in a parabolic-elliptic system of mathematical biology, Adv. Differential Equations 6 (2001), 21-50.
    • (2001) Adv. Differential Equations , vol.6 , pp. 21-50
    • Senba, T.1    Suzuki, T.2
  • 35
    • 0010915457 scopus 로고    scopus 로고
    • Parabolic system of chemotaxis: Blow-up in a finite and the infinite time
    • T. Senba and T. Suzuki, Parabolic system of chemotaxis: blow-up in a finite and the infinite time, Methods Appl. Anal. 8 (2001).
    • (2001) Methods Appl. Anal , vol.8
    • Senba, T.1    Suzuki, T.2
  • 36
    • 0001358147 scopus 로고
    • A symmetry problem in potential theory
    • J. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal. 43 (1971), 304-318.
    • (1971) Arch. Rational Mech. Anal , vol.43 , pp. 304-318
    • Serrin, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.