메뉴 건너뛰기




Volumn 180, Issue 2, 2006, Pages 293-330

Bifurcation From Stability to Instability for a Free Boundary Problem Arising in a Tumor Model

Author keywords

Cell Density; Complex System; Neural Network; Tumor Cell; Tumor Growth

Indexed keywords


EID: 85130332650     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-005-0408-z     Document Type: Article
Times cited : (116)

References (25)
  • 3
    • 0025068944 scopus 로고
    • Adam, J.A., Maggelakis, S.A.: Diffusion regulated growth characteristics of a spherical prevascular carcinoma. Bull. Math. Biol. 52, 549–582 (1990) DOI: 10.1016/S0092-8240(05)80362-3
    • (1990) Bull. Math. Biol. , vol.52 , pp. 549
    • Adam1
  • 4
    • 0038384640 scopus 로고    scopus 로고
    • Bazaliy, B.V., Friedman, A.: A free boundary problem for elliptic-parabolic system: application to a model of tumor growth. Comm. Partial Differential Equations. 28, 517-560, (2003) DOI: 10.1081/PDE-120020486
    • (2003) Comm. Partial Differential Equations. , vol.28 , pp. 517
    • Bazaliy1
  • 5
    • 0242679755 scopus 로고    scopus 로고
    • Bazaliy, B.V., Friedman, A.: Global existence and asymptotic stability for an elliptic-parabolic free boundary problem: an application to a model of tumor growth. Indiana Univ. Math. J. 52, 1265–1304, (2003) DOI: 10.1512/iumj.2003.52.2317
    • (2003) Indiana Univ. Math. J. , vol.52 , pp. 1265
    • Bazaliy1
  • 6
    • 0027395356 scopus 로고
    • Britton, N., Chaplain, M.A.J.: A qualitative analysis of some models of tissue growth. Math. Biosci. 113, 77–89 (1993) DOI: 10.1016/0025-5564(93)90009-Y
    • (1993) Math. Biosci. , vol.113 , pp. 77
    • Britton1
  • 7
    • 0031309511 scopus 로고    scopus 로고
    • Byrne, H.M.: The importance of intercellular adhesion in the development of carcinomas. IMA J. Math. Appl. Med. Biol. 14, 305–323 (1997)
    • (1997) IMA J. Math. Appl. Med. Biol. , vol.14 , pp. 305
    • Byrne1
  • 8
    • 0033158956 scopus 로고    scopus 로고
    • Byrne, H.M.: A weakly nonlinear analysis of a model of avascular solid tumor growth. J. Math. Biol. 39, 59–89, (1999) DOI: 10.1007/s002850050163
    • (1999) J. Math. Biol. , vol.39 , pp. 59
    • Byrne1
  • 9
    • 0028790729 scopus 로고
    • Byrne, H.M., Chaplain, M.A.J.: Growth of nonnecrotic tumors in the presence and absence of inhibitors. Math. Biosci. 130, 151–181, (1995) DOI: 10.1016/0025-5564(94)00117-3
    • (1995) Math. Biosci. , vol.130 , pp. 151
    • Byrne1
  • 10
    • 0030431867 scopus 로고    scopus 로고
    • Byrne, H.M., Chaplain, M.A.J.: Modelling the role of cell-cell adhesion in the growth and development of carcinomas. Math. Comput. Modelling. 24, 35–55, (1996) DOI: 10.1016/S0895-7177(96)00174-4
    • (1996) Math. Comput. Modelling. , vol.24 , pp. 35
    • Byrne1
  • 11
    • 0030586186 scopus 로고    scopus 로고
    • Byrne, H.M., Chaplain, M.A.J.: Growth of nonnecrotic tumors in the presence and absence of inhibitors. Math. Biosci. 135, 187–216, (1996) DOI: 10.1016/0025-5564(96)00023-5
    • (1996) Math. Biosci. , vol.135 , pp. 187
    • Byrne1
  • 13
    • 3142764638 scopus 로고    scopus 로고
    • Chen, A., Friedman, A.: A free boundary problem for elliptic-hyperbolic system: an application to tumor growth. SIAM J. Math. Anal. 35, 974–986 (2003) DOI: 10.1137/S0036141002418388
    • (2003) SIAM J. Math. Anal. , vol.35 , pp. 974
    • Chen1
  • 15
    • 0142028939 scopus 로고    scopus 로고
    • Fontelos, M., Friedman, A.: Symmetry-breaking bifurcations of free boundary problems in three dimensions. Asymptot. Anal. 35, 187–206, (2003)
    • (2003) Asymptot. Anal. , vol.35 , pp. 187
    • Fontelos1
  • 16
    • 2442669044 scopus 로고    scopus 로고
    • Fontelos, M., Friedman, A.: Symmetry-breaking bifurcations of chagred drops. Arch. Ration. Mech. Anal. 172, 267–294, (2004) DOI: 10.1007/s00205-003-0298-x
    • (2004) Arch. Ration. Mech. Anal. , vol.172 , pp. 267
    • Fontelos1
  • 17
    • 0033094895 scopus 로고    scopus 로고
    • Friedman, A., Reitich, F.: Analysis of a mathematical model for growth of tumor. J. Math. Biol. 38, 262–284, (1999) DOI: 10.1007/s002850050149
    • (1999) J. Math. Biol. , vol.38 , pp. 262
    • Friedman1
  • 18
    • 0242588180 scopus 로고    scopus 로고
    • Friedman, A., Reitich, F.: Symmetry-breaking bifurcation of analytic solutions to free boundary problems: an application to a model of tumor growth. Trans. Amer. Math. Soc. 353, 1587–1634, (2000) DOI: 10.1090/S0002-9947-00-02715-X
    • (2000) Trans. Amer. Math. Soc. , vol.353 , pp. 1587
    • Friedman1
  • 19
    • 0000990726 scopus 로고    scopus 로고
    • Friedman, A., Reitich, F.: Nonlinear stability of a quasi-static Stefan problem with surface tension: a continuation approach. Ann. Sc. Norm. Super. Pisa Cl. Sci. 30, 341–403, (2001)
    • (2001) Ann. Sc. Norm. Super. Pisa Cl. Sci. , vol.30 , pp. 341
    • Friedman1
  • 20
    • 0000128125 scopus 로고
    • Greenspan, H.P.: Models for the growth of a solid tumor by diffusion. Stud. Appl. Math. 52, 317–340, (1972)
    • (1972) Stud. Appl. Math. , vol.52 , pp. 317
    • Greenspan1
  • 21
    • 0017198676 scopus 로고
    • Greenspan, H.P.: On the growth of cell culture and solid tumors. J. Theoret. Biol. 56, 229–242, (1976)
    • (1976) J. Theoret. Biol. , vol.56 , pp. 229
    • Greenspan1
  • 22
    • 0025627956 scopus 로고
    • Maggelakis, S.A., Adam, J.A.: Mathematical model for prevasculat growth of a spherical carcinoma. Math. Comp. Modelling. 13, 23–38, (1990) DOI: 10.1016/0895-7177(90)90040-T
    • (1990) Math. Comp. Modelling. , vol.13 , pp. 23
    • Maggelakis1
  • 23
    • 0017806209 scopus 로고
    • McEwain, D.L.S., Morris, L.E.: Apoptosis as a volume loss mechanism in mathematical models of solid tumor growth. Math. Biosci. 39, 147–157, (1978) DOI: 10.1016/0025-5564(78)90033-0
    • (1978) Math. Biosci. , vol.39 , pp. 147
    • McEwain1
  • 25
    • 85130364956 scopus 로고
    • Dynamical systems (Proc. Internat. Sympos., Univ. Florida, Gainesville, Fla., 1976). Academic Press, New York
    • Weinberger, H.F.: The stability of solutions bifurcating from steady or periodic solutions. Dynamical systems (Proc. Internat. Sympos., Univ. Florida, Gainesville, Fla., 1976). Academic Press, New York, 349–366, 1977
    • (1977) The stability of solutions bifurcating from steady or periodic solutions , pp. 349-366
    • Weinberger, H.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.