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Volumn 97, Issue 1-2, 1998, Pages 99-119

Self-similar blow-up for a reaction-diffusion system

Author keywords

Blow up; Matched asymptotic expansions; Reaction diffusion systems; Self similar behaviour

Indexed keywords

MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

EID: 0032154585     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(98)00104-6     Document Type: Article
Times cited : (93)

References (17)
  • 1
    • 0000657461 scopus 로고    scopus 로고
    • Local and global solvability of some parabolic systems modelling chemotaxis
    • to appear
    • [1] P. Biler, Local and global solvability of some parabolic systems modelling chemotaxis, Adv. Math. Sci. Appl., to appear.
    • Adv. Math. Sci. Appl.
    • Biler, P.1
  • 2
    • 0019784884 scopus 로고
    • Nonlinear aspects of chemotaxis
    • [2] 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
  • 3
    • 0022113843 scopus 로고
    • Analysis of the early stage of thermal runaway
    • [3] J.W. Dold, Analysis of the early stage of thermal runaway, Quart. J. Mech. Appl. Math. 38 (1985) 361-387.
    • (1985) Quart. J. Mech. Appl. Math. , vol.38 , pp. 361-387
    • Dold, J.W.1
  • 4
    • 84990616610 scopus 로고
    • Asymptotically self-similar blow-up of semilinear heat equations
    • [4] Y. Giga, R.V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations, Comm. Pure Appl. Math. 38 (1985) 297-319.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 297-319
    • Giga, Y.1    Kohn, R.V.2
  • 5
    • 0010505120 scopus 로고
    • Application of new comparison theorems in the investigation of unbounded solutions of nonlinear parabolic equations
    • [5] V.A. Galaktionov, S.A. Posashkov, Application of new comparison theorems in the investigation of unbounded solutions of nonlinear parabolic equations, Differential Equations 22 (7) (1986) 1165-1173.
    • (1986) Differential Equations , vol.22 , Issue.7 , pp. 1165-1173
    • Galaktionov, V.A.1    Posashkov, S.A.2
  • 6
    • 0039712703 scopus 로고    scopus 로고
    • Singularity patterns in a chemotaxis model
    • [6] M.A. Herrero, J.J.L. Velázquez, Singularity patterns in a chemotaxis model, Math. Ann. 306 (3) (1996) 583-623.
    • (1996) Math. Ann. , vol.306 , Issue.3 , pp. 583-623
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 7
    • 0030334089 scopus 로고    scopus 로고
    • Chemotactic collapse for the Keller-Segel model
    • [7] M.A. Herrero, J.J.L. Velázquez, Chemotactic collapse for the Keller-Segel model. J. Math. Biol. 35 (1996) 177-194.
    • (1996) J. Math. Biol. , vol.35 , pp. 177-194
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 9
    • 0000507343 scopus 로고    scopus 로고
    • Finite-time aggregation into a single point in a reaction-diffusion system
    • [9] M.A. Herrero, E. Medina, J.J.L. Velázquez, Finite-time aggregation into a single point in a reaction-diffusion system, Nonlinearity 10 (1997) 1739-1754.
    • (1997) Nonlinearity , vol.10 , pp. 1739-1754
    • Herrero, M.A.1    Medina, E.2    Velázquez, J.J.L.3
  • 10
    • 84966208077 scopus 로고
    • On explosions of solutions to a system of partial differential equations modelling chemotaxis
    • [10] W. Jäger, S. Luckhaus, On explosions of solutions to a system of partial differential equations modelling chemotaxis, Trans. Amer. Math. Soc. 329 (2) (1992) 819-824.
    • (1992) Trans. Amer. Math. Soc. , vol.329 , Issue.2 , pp. 819-824
    • Jäger, W.1    Luckhaus, S.2
  • 11
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • [11] E.F. Keller, 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
  • 12
    • 84971178534 scopus 로고
    • The form of blow-up for nonlinear parabolic equations
    • [12] A.A. Lacey, The form of blow-up for nonlinear parabolic equations, Proc. Roy. Soc. Edinburg A 98 (1984) 183-202.
    • (1984) Proc. Roy. Soc. Edinburg A , vol.98 , pp. 183-202
    • Lacey, A.A.1
  • 13
    • 0000911254 scopus 로고
    • Blow-up of radially symmetric solutions to a chemotaxis system
    • [13] T. Nagai, Blow-up of radially symmetric solutions to a chemotaxis system, Adv. Math. Sci. Appl. (1995) 1-21.
    • (1995) Adv. Math. Sci. Appl. , pp. 1-21
    • Nagai, T.1
  • 14
    • 0015757937 scopus 로고
    • Chemotaxis signal relaying and aggregation morphology
    • [14] V. Nanjundiah, Chemotaxis signal relaying and aggregation morphology, J. Theor. Biology 42 (1973) 63-105.
    • (1973) J. Theor. Biology , vol.42 , pp. 63-105
    • Nanjundiah, V.1
  • 15
    • 84968503478 scopus 로고
    • Classification of singularities for blowing-up solutions in higher dimensions
    • [15] J.J.L. Velázquez, Classification of singularities for blowing-up solutions in higher dimensions, Trans. Amer. Math. Soc. 338 (1) (1993) 441-464.
    • (1993) Trans. Amer. Math. Soc. , vol.338 , Issue.1 , pp. 441-464
    • Velázquez, J.J.L.1
  • 16
    • 21144461798 scopus 로고
    • On steady distributions of self-attracting clusters under friction and
    • [16] G. Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch. Rat. Mech. Anal. 119 (1992) 355-391.
    • (1992) Arch. Rat. Mech. Anal. , vol.119 , pp. 355-391
    • Wolansky, G.1
  • 17
    • 51249166872 scopus 로고
    • On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity
    • [17] G. Wolansky, On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity, J. Anal. Math. 59 (1992) 251-272.
    • (1992) J. Anal. Math. , vol.59 , pp. 251-272
    • Wolansky, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.