메뉴 건너뛰기




Volumn 33, Issue 4, 2008, Pages 636-655

Asymptotic behaviour of solutions of a multidimensional moving boundary problem modeling tumor growth

Author keywords

Centre manifold; Moving boundary problem; Stability; Surface tension; Tumor growth

Indexed keywords


EID: 41849134265     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605300701743848     Document Type: Article
Times cited : (72)

References (35)
  • 1
    • 0001835099 scopus 로고
    • Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems
    • Schmeisser, H. J, Triebel, H, eds, Teubner, pp
    • Amann, H. (1993). Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. In: Schmeisser, H. J., Triebel, H., eds. Function Spaces, Differential Operators and Nonlinear Analysis. Teubner, pp. 9-126.
    • (1993) Function Spaces, Differential Operators and Nonlinear Analysis , pp. 9-126
    • Amann, H.1
  • 2
    • 0007292463 scopus 로고    scopus 로고
    • Stefan problem for the Laplace equation with regard for the curvature of the free boundary
    • Bazaliy, B. (1997). Stefan problem for the Laplace equation with regard for the curvature of the free boundary. Ukrainian Math. J. 49:1465-1484.
    • (1997) Ukrainian Math. J , vol.49 , pp. 1465-1484
    • Bazaliy, B.1
  • 3
    • 0038384640 scopus 로고    scopus 로고
    • A free boundary problem for an elliptic-parabolic system: Application to a model of tumor growth
    • Bazaliy, B., Friedman, A. (2003a). A free boundary problem for an elliptic-parabolic system: application to a model of tumor growth. Comm. Partial Differential Equations 28(3-4):517-560.
    • (2003) Comm. Partial Differential Equations , vol.28 , Issue.3-4 , pp. 517-560
    • Bazaliy, B.1    Friedman, A.2
  • 4
    • 0242679755 scopus 로고    scopus 로고
    • Global existence and asymptotic stability for an ellipticparabolic free boundary problem: An application to a model of tumor growth
    • Bazaliy, B., Friedman, A. (2003b). Global existence and asymptotic stability for an ellipticparabolic free boundary problem: an application to a model of tumor growth. Indiana Univ. Math. J. 52(5): 1265-1304.
    • (2003) Indiana Univ. Math. J , vol.52 , Issue.5 , pp. 1265-1304
    • Bazaliy, B.1    Friedman, A.2
  • 5
    • 0033158956 scopus 로고    scopus 로고
    • A weakly nonlinear analysis of a model of avascular solid tumor growth
    • Byrne, H. M. (1999). A weakly nonlinear analysis of a model of avascular solid tumor growth. J. Math. Biol. 39:59-89.
    • (1999) J. Math. Biol , vol.39 , pp. 59-89
    • Byrne, H.M.1
  • 6
    • 0028790729 scopus 로고
    • Growth of nonnecrotic tumors in the presence and absence of inhibitors
    • Byrne, H. M., Chaplain, M. A. J. (1995). Growth of nonnecrotic tumors in the presence and absence of inhibitors. Math. Biosci. 130:151-181.
    • (1995) Math. Biosci , vol.130 , pp. 151-181
    • Byrne, H.M.1    Chaplain, M.A.J.2
  • 7
    • 0001649885 scopus 로고    scopus 로고
    • Existence, uniqueness and regularity of classical solutions of the Mullins-Sekerka problem
    • Chen, X., Hong, J., Yi, F. (1997). Existence, uniqueness and regularity of classical solutions of the Mullins-Sekerka problem. Comm. Partial Differential Equations 21:1705-1727.
    • (1997) Comm. Partial Differential Equations , vol.21 , pp. 1705-1727
    • Chen, X.1    Hong, J.2    Yi, F.3
  • 8
    • 0036584916 scopus 로고    scopus 로고
    • Analysis of a mathematical model for the growth of tumors under the action of external inhibitors
    • Cui, S. (2002). Analysis of a mathematical model for the growth of tumors under the action of external inhibitors. J. Math. Biol. 44:395-426.
    • (2002) J. Math. Biol , vol.44 , pp. 395-426
    • Cui, S.1
  • 9
    • 27144544441 scopus 로고    scopus 로고
    • Analysis of a free boundary problem modeling tumor growth
    • Cui, S. (2005a). Analysis of a free boundary problem modeling tumor growth. Acta Math. Sinica (English Series) 21:1071-1082.
    • (2005) Acta Math. Sinica (English Series) , vol.21 , pp. 1071-1082
    • Cui, S.1
  • 10
    • 22544467766 scopus 로고    scopus 로고
    • Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors
    • Cui, S. (2005b). Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors. Interfaces and Free Boundaries 7:147-159.
    • (2005) Interfaces and Free Boundaries , vol.7 , pp. 147-159
    • Cui, S.1
  • 11
    • 33750606138 scopus 로고    scopus 로고
    • Existence of a stationary solution for the modified ward-King tumor growth model
    • Cui, S. (2006). Existence of a stationary solution for the modified ward-King tumor growth model. Advances Appl. Math. 36:421-445.
    • (2006) Advances Appl. Math , vol.36 , pp. 421-445
    • Cui, S.1
  • 12
    • 41849108874 scopus 로고    scopus 로고
    • Well-posedness and stability of a multi-dimensional tumor growth model
    • Submitted
    • Cui, S., Escher, J. Well-posedness and stability of a multi-dimensional tumor growth model. Submitted.
    • Cui, S.1    Escher, J.2
  • 13
    • 0034040582 scopus 로고    scopus 로고
    • Analysis of a mathematical model of the effect of inhibitors on the growth of tumors
    • Cui, S., Friedman, A. (2000). Analysis of a mathematical model of the effect of inhibitors on the growth of tumors. Math. Biosci. 164:103-137.
    • (2000) Math. Biosci , vol.164 , pp. 103-137
    • Cui, S.1    Friedman, A.2
  • 14
    • 0035869870 scopus 로고    scopus 로고
    • Analysis of a mathematical model of the growth of necrotic tumors
    • Cui, S., Friedman, A. (2001). Analysis of a mathematical model of the growth of necrotic tumors. J. Math. Anal. Appl. 255:636-677.
    • (2001) J. Math. Anal. Appl , vol.255 , pp. 636-677
    • Cui, S.1    Friedman, A.2
  • 15
    • 0042363716 scopus 로고    scopus 로고
    • A free boundary problem for a singular system of differential equations: An application to a model of tumor growth
    • Cui, S., Friedman, A. (2002). A free boundary problem for a singular system of differential equations: an application to a model of tumor growth. Trans. Amer. Math. Soc. 355:3537-3590.
    • (2002) Trans. Amer. Math. Soc , vol.355 , pp. 3537-3590
    • Cui, S.1    Friedman, A.2
  • 16
    • 84979081677 scopus 로고    scopus 로고
    • A hyperbolic free boundary problem modeling tumor growth
    • Cui, S., Friedman, A. (2003). A hyperbolic free boundary problem modeling tumor growth. Interfaces and Free Boundaries. 5:159-181.
    • (2003) Interfaces and Free Boundaries , vol.5 , pp. 159-181
    • Cui, S.1    Friedman, A.2
  • 17
    • 27844600157 scopus 로고    scopus 로고
    • Global existence for a parabolic-hyperbolic free boundary problem modeling tumor growth
    • Cui, S., Wei, X. (2005). Global existence for a parabolic-hyperbolic free boundary problem modeling tumor growth. Acta Math. Appl. Sinica (English Series) 21:3537-3590.
    • (2005) Acta Math. Appl. Sinica (English Series) , vol.21 , pp. 3537-3590
    • Cui, S.1    Wei, X.2
  • 18
    • 39449127707 scopus 로고    scopus 로고
    • Bifurcation analysis of an elliptic free boundary problem modelling the growth of avascular tumors
    • Cui, S., Escher, J. (2007). Bifurcation analysis of an elliptic free boundary problem modelling the growth of avascular tumors. SIAM J. Math. Anal. 39:210-235.
    • (2007) SIAM J. Math. Anal , vol.39 , pp. 210-235
    • Cui, S.1    Escher, J.2
  • 19
    • 0002500168 scopus 로고
    • Equations d'évolution abstraites nonlinéaires de type parabolique.
    • Da Prato, G., Grisvard, P. (1979). Equations d'évolution abstraites nonlinéaires de type parabolique. Ann. Mat. Pura Appl. 120:329-396.
    • (1979) Ann. Mat. Pura Appl , vol.120 , pp. 329-396
    • Da Prato, G.1    Grisvard, P.2
  • 21
    • 3242743726 scopus 로고    scopus 로고
    • Classical solutions to a moving boundary problem for an elliptic-parabolic system
    • Escher, J. (2004). Classical solutions to a moving boundary problem for an elliptic-parabolic system. Interfaces Free and Boundaries 6:175-193.
    • (2004) Interfaces Free and Boundaries , vol.6 , pp. 175-193
    • Escher, J.1
  • 22
    • 0000010015 scopus 로고    scopus 로고
    • Classical solutions for Hele-Shaw models with surface tension
    • Escher, J., Simonett, G. (1997a). Classical solutions for Hele-Shaw models with surface tension. Adv. Diff. Equa. 2:619-642.
    • (1997) Adv. Diff. Equa , vol.2 , pp. 619-642
    • Escher, J.1    Simonett, G.2
  • 23
    • 0031478022 scopus 로고    scopus 로고
    • Classical solutions of multidimensional Hele-Shaw models
    • Escher, J., Simonett, G. (1997b). Classical solutions of multidimensional Hele-Shaw models. SIAM J. Math. Anal. 28:1028-1047.
    • (1997) SIAM J. Math. Anal , vol.28 , pp. 1028-1047
    • Escher, J.1    Simonett, G.2
  • 24
    • 22044436278 scopus 로고    scopus 로고
    • The volume preserving mean curvature flow near spheres
    • Escher, J., Simonett, G. (1998a). The volume preserving mean curvature flow near spheres. Proc. Amer. Math. Soc. 126:2789-2796.
    • (1998) Proc. Amer. Math. Soc , vol.126 , pp. 2789-2796
    • Escher, J.1    Simonett, G.2
  • 25
    • 0001025274 scopus 로고    scopus 로고
    • A centre manifold analysis for the Mullins-Sekerka model
    • Escher, J., Simonett, G. (1998b). A centre manifold analysis for the Mullins-Sekerka model. J. Differential Equations 143:267-292.
    • (1998) J. Differential Equations , vol.143 , pp. 267-292
    • Escher, J.1    Simonett, G.2
  • 26
    • 0033094895 scopus 로고    scopus 로고
    • Analysis of a mathematical model for the growth of tumors
    • Friedman, A., Reitich, F. (1999). Analysis of a mathematical model for the growth of tumors. J. Math. Biol. 38:262-284.
    • (1999) J. Math. Biol , vol.38 , pp. 262-284
    • Friedman, A.1    Reitich, F.2
  • 27
    • 0242588180 scopus 로고    scopus 로고
    • Symmetry-breaking bifurcation of analytic solutions to free boundary problems
    • Friedman, A., Reitich, F. (2000a). Symmetry-breaking bifurcation of analytic solutions to free boundary problems. Trans. Amer. Math. Soc. 353:1587-1634.
    • (2000) Trans. Amer. Math. Soc , vol.353 , pp. 1587-1634
    • Friedman, A.1    Reitich, F.2
  • 28
    • 0035634058 scopus 로고    scopus 로고
    • On the existence of spatially patterned dormant malignancies in the model for the growth of non-necrotic vascular tumor
    • Friedman, A., Reitich, F. (2000b). On the existence of spatially patterned dormant malignancies in the model for the growth of non-necrotic vascular tumor. Math. Models Appl. Sci. 11:601-625.
    • (2000) Math. Models Appl. Sci , vol.11 , pp. 601-625
    • Friedman, A.1    Reitich, F.2
  • 29
    • 0142028939 scopus 로고    scopus 로고
    • Symmetric-breaking bifurcations of free boundary problems in three dimensions
    • Friedman, A., Fontelos, M. (2003). Symmetric-breaking bifurcations of free boundary problems in three dimensions. Asymptot. Anal. 35:187-206.
    • (2003) Asymptot. Anal , vol.35 , pp. 187-206
    • Friedman, A.1    Fontelos, M.2
  • 30
    • 85130332650 scopus 로고    scopus 로고
    • Bifurcation from stability to instability for a free boundary problem arising in a tumor model
    • Friedman, A., Hu, B. (2006a). Bifurcation from stability to instability for a free boundary problem arising in a tumor model. Arch. Rat. Mech. Anal. 180:293-330.
    • (2006) Arch. Rat. Mech. Anal , vol.180 , pp. 293-330
    • Friedman, A.1    Hu, B.2
  • 31
    • 33646686604 scopus 로고    scopus 로고
    • Asymptotic stability for a free boundary problem arising in a tumor model
    • Friedman, A., Hu, B. (2006b). Asymptotic stability for a free boundary problem arising in a tumor model. J. Differential Equations 227:598-639.
    • (2006) J. Differential Equations , vol.227 , pp. 598-639
    • Friedman, A.1    Hu, B.2
  • 32
    • 0017198676 scopus 로고
    • On the growth and stability of cell cultures and solid tumors
    • Greenspan, H. (1976). On the growth and stability of cell cultures and solid tumors. J. Theor. Biol. 56:229-242.
    • (1976) J. Theor. Biol , vol.56 , pp. 229-242
    • Greenspan, H.1
  • 35
    • 0031087466 scopus 로고    scopus 로고
    • Mathematical modelling of avascular tumor growth
    • Ward, J. P., King, J. R. (1997). Mathematical modelling of avascular tumor growth. IMA J. Math. Appl. Med. Biol. 14:39-70.
    • (1997) IMA J. Math. Appl. Med. Biol , vol.14 , pp. 39-70
    • Ward, J.P.1    King, J.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.