메뉴 건너뛰기




Volumn 272, Issue 1, 2002, Pages 138-163

Stability of solutions of chemotaxis equations in reinforced random walks

Author keywords

Chemotaxis; Parabolic equations; Reinforced random walk; Stability of stationary solutions

Indexed keywords


EID: 0036700354     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00147-6     Document Type: Article
Times cited : (89)

References (22)
  • 1
    • 0000656670 scopus 로고
    • Orientation of cells migrating in a chemotactic gradient
    • Springer-Verlag, New York
    • W. Alt, Orientation of cells migrating in a chemotactic gradient, in: Biological Growth and Spread, Lecture Notes in Biomath., Vol. 38, Springer-Verlag, New York, 1980, pp. 353-366.
    • (1980) Biological Growth and Spread, Lecture Notes in Biomath , vol.38 , pp. 353-366
    • Alt, W.1
  • 2
    • 0019188958 scopus 로고
    • Biased random walk models for chemotaxis and related diffusion approximations
    • W. Alt, Biased random walk models for chemotaxis and related diffusion approximations, J. Math. Biol. 9 (1980) 147-177.
    • (1980) J. Math. Biol , vol.9 , pp. 147-177
    • Alt, W.1
  • 3
    • 0032170064 scopus 로고    scopus 로고
    • Continuous and discrete mathematical models of tumor-induced angiogenesis
    • A.R.A. Anderson, M.A.I. Chaplain, Continuous and discrete mathematical models of tumor-induced angiogenesis, Bull. Math. Biol. 60 (1998) 857-899.
    • (1998) Bull. Math. Biol , vol.60 , pp. 857-899
    • Anderson, A.R.A.1    Chaplain, M.A.I.2
  • 5
    • 0036433997 scopus 로고    scopus 로고
    • Mathematical analysis of a model for the initiation of angiogenesis
    • to appear
    • M.A. Fontelos, A. Friedman, B. Hu, Mathematical analysis of a model for the initiation of angiogenesis, SIAM J. Math. Anal., to appear.
    • SIAM J. Math. Anal
    • Fontelos, M.A.1    Friedman, A.2    Hu, B.3
  • 6
    • 0000383513 scopus 로고    scopus 로고
    • Global behavior of a reaction-diffusion system modeling chemotaxis
    • H. Gajewsky, K. Zacharias, Global behavior of a reaction-diffusion system modeling chemotaxis, Math. Nachr. 195 (1998) 177-194.
    • (1998) Math. Nachr , vol.195 , pp. 177-194
    • Gajewsky, H.1    Zacharias, K.2
  • 7
    • 0030334089 scopus 로고    scopus 로고
    • Chemotactic collapse for the Keller-Seller model
    • M.A. Herrero, J.J.L. Velázquez, Chemotactic collapse for the Keller-Seller 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
  • 8
    • 0039712703 scopus 로고    scopus 로고
    • Singularity patterns in a chemotaxis model
    • M.A. Herrero, 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
  • 10
    • 84966208077 scopus 로고
    • On explosions of solutions to a system of partial differential equations modeling chemotaxis
    • W. Jäger, S. Luckhaus, On explosions of solutions to a system of partial differential equations modeling 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
  • 11
    • 0015011285 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. 30 (1971) 225-234.
    • (1971) J. Theoret. Biol , vol.30 , pp. 225-234
    • Keller, E.F.1    Segel, L.A.2
  • 13
    • 0003223550 scopus 로고
    • Linear and Quasilinear Equations of Parabolic Type
    • American Mathematical Society, Providence, RI
    • D.A. Ladyẑenskaja, V.A. Solonnikov, N.N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, Transl. Amer. Math. Soc., American Mathematical Society, Providence, RI, 1968.
    • (1968) Transl. Amer. Math. Soc
    • Ladyẑenskaja, D.A.1    Solonnikov, V.A.2    Uraltseva, N.N.3
  • 14
    • 0011014828 scopus 로고    scopus 로고
    • Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma
    • to appear
    • H.A. Levine, S. Pamuk, B.P. Sleeman, M. Nilsen-Hamilton, Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma, to appear.
    • Levine, H.A.1    Pamuk, S.2    Sleeman, B.P.3    Nilsen-Hamilton, M.4
  • 15
    • 0031162898 scopus 로고    scopus 로고
    • A system of reaction diffusion equation arising in the theory of reinforced random walks
    • H.A. Levine, B.D. Sleeman, A system of reaction diffusion equation 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
  • 16
    • 0033731143 scopus 로고    scopus 로고
    • A mathematical modeling for the roles of pericytes and macrophages in the initiation of angiogenesis I. The role of protease inhibitors in preventing angiogenesis
    • H.A. Levine, B.P. Sleeman, M. Nilsen-Hamilton, A mathematical modeling for the roles of pericytes and macrophages in the initiation of angiogenesis I. The role of protease inhibitors in preventing angiogenesis, Math. Biosci. 168 (2000) 75-115.
    • (2000) Math. Biosci , vol.168 , pp. 75-115
    • Levine, H.A.1    Sleeman, B.P.2    Nilsen-Hamilton, M.3
  • 18
    • 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, Math. Methods Appl. Sci. (1995) 581-601.
    • (1995) Math. Methods Appl. Sci , pp. 581-601
    • Nagai, T.1
  • 19
    • 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
  • 20
    • 0001373727 scopus 로고
    • Stationary solutions of chemotaxis equations
    • R. Schaaf, Stationary solutions of chemotaxis equations, Trans. Amer. Math. Soc. 292 (1985) 531-556.
    • (1985) Trans. Amer. Math. Soc , vol.292 , pp. 531-556
    • Schaaf, R.1
  • 21
    • 0034455986 scopus 로고    scopus 로고
    • The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems
    • A. Stevens, The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems, SIAM J. Appl. Math. 61 (2000) 183-212.
    • (2000) SIAM J. Appl. Math , vol.61 , pp. 183-212
    • Stevens, A.1
  • 22
    • 0000646419 scopus 로고    scopus 로고
    • A critical parabolic estimate and application to nonlocal equations arising in chemotaxis
    • G. Wolansky, A critical parabolic estimate and application to nonlocal equations arising in chemotaxis, Appl. Anal. 66 (1997) 291-321.
    • (1997) Appl. Anal , vol.66 , pp. 291-321
    • Wolansky, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.