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Volumn 21, Issue 4, 2005, Pages 597-614

Global existence for a parabolic-hyperbolic free boundary problem modelling tumor growth

Author keywords

Existence; Free boundary problem; Global solution; Tumor growth; Uniqueness

Indexed keywords


EID: 27844600157     PISSN: 01689673     EISSN: 16183932     Source Type: Journal    
DOI: 10.1007/s10255-005-0268-1     Document Type: Article
Times cited : (31)

References (22)
  • 1
    • 0028790729 scopus 로고
    • Growth of nonnecrotic tumors in the presence and absence of inhibitors
    • Byrne, H., Chaplain, M. Growth of nonnecrotic tumors in the presence and absence of inhibitors. Math. Biosci., 130: 151-181 (1995)
    • (1995) Math. Biosci. , vol.130 , pp. 151-181
    • Byrne, H.1    Chaplain, M.2
  • 2
    • 0030586186 scopus 로고    scopus 로고
    • Growth of necrotic tumors in the presence and absence of inhibitors
    • Byrne, H., Chaplain, M. Growth of necrotic tumors in the presence and absence of inhibitors. Math. Biosci., 135: 187-216 (1996)
    • (1996) Math. Biosci. , vol.135 , pp. 187-216
    • Byrne, H.1    Chaplain, M.2
  • 3
    • 0031320752 scopus 로고    scopus 로고
    • Free boundary value problems associated with the growth and development of multicellular spheroids
    • Byrne, H., Chaplain, M. Free boundary value problems associated with the growth and development of multicellular spheroids. Euro. J. Appl. Math., 8: 639-658 (1997)
    • (1997) Euro. J. Appl. Math. , vol.8 , pp. 639-658
    • Byrne, H.1    Chaplain, M.2
  • 4
    • 0036584916 scopus 로고    scopus 로고
    • Analysis of a mathematical model for the growth of tumors under the action of external inhibitors
    • Cui, S. Analysis of a mathematical model for the growth of tumors under the action of external inhibitors. J. Math. Biol., 44: 395-426 (2002)
    • (2002) J. Math. Biol. , vol.44 , pp. 395-426
    • Cui, S.1
  • 5
    • 0034040582 scopus 로고    scopus 로고
    • Analysis of a mathematical model of the effect of inhibitors on the growth of bumors
    • Cui, S. and Friedman, A.. Analysis of a mathematical model of the effect of inhibitors on the growth of bumors. Math. Bioaci., 164: 103-137 (2000)
    • (2000) Math. Bioaci. , vol.164 , pp. 103-137
    • Cui, S.1    Friedman, A.2
  • 6
    • 0035869870 scopus 로고    scopus 로고
    • Analysis of a mathematical model of the growth of necrotic tumors
    • Cui, S., Friedman, A. Analysis of a mathematical model of the growth of necrotic tumors. J. Math. Anal. Appl. 255: 636-677 (2001)
    • (2001) J. Math. Anal. Appl. , vol.255 , pp. 636-677
    • Cui, S.1    Friedman, A.2
  • 7
    • 27844580183 scopus 로고    scopus 로고
    • Analysis of a mathematical model of the direct effect of inhibitors on the growth of tumors
    • Chinese Series
    • Cui, S. and Ai, J.. Analysis of a mathematical model of the direct effect of inhibitors on the growth of tumors. Acta Math. Appl. Sinica, 25: 617-625 (2002) (Chinese Series)
    • (2002) Acta Math. Appl. Sinica , vol.25 , pp. 617-625
    • Cui, S.1    Ai, J.2
  • 8
    • 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. 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)
    • (2002) Trans. Amer. Math. Soc. , vol.355 , pp. 3537-3590
    • Cui, S.1    Friedman, A.2
  • 9
    • 84979081677 scopus 로고    scopus 로고
    • A hyperbolic free boundary problem modeling tumor growth
    • Cui, S., Friedman, A. A hyperbolic free boundary problem modeling tumor growth. Interfaces and Free Boundaries, 5: 159-181 (2003)
    • (2003) Interfaces and Free Boundaries , vol.5 , pp. 159-181
    • Cui, S.1    Friedman, A.2
  • 10
    • 1042279440 scopus 로고    scopus 로고
    • A hierarchy of cancer models and their mathematical challenges
    • Friedman, A. A hierarchy of cancer models and their mathematical challenges. Disc. Cont. Dyna. Syst., 4: 147-159 (2004)
    • (2004) Disc. Cont. Dyna. Syst. , vol.4 , pp. 147-159
    • Friedman, A.1
  • 11
    • 0033094895 scopus 로고    scopus 로고
    • Analysis of a mathematical model for the growth of tumors
    • Friedman, A., Reitich, F. Analysis of a mathematical model for the growth of tumors. J. Math. Biol. 38: 262-284 (1999)
    • (1999) J. Math. Biol. , vol.38 , pp. 262-284
    • Friedman, A.1    Reitich, F.2
  • 12
    • 0242588180 scopus 로고    scopus 로고
    • Symmetry-breaking bifurcation of analytic solutions to free boundary problems
    • Friedman, A., Reitich, F. Symmetry-breaking bifurcation of analytic solutions to free boundary problems. Trans. Amer. Math. Soc., 353: 1587-1634 (2000)
    • (2000) Trans. Amer. Math. Soc. , vol.353 , pp. 1587-1634
    • Friedman, A.1    Reitich, F.2
  • 13
    • 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., Reitech, F. 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)
    • (2000) Math. Models Appl. Sci. , vol.11 , pp. 601-625
    • Friedman, A.1    Reitech, F.2
  • 14
    • 0000128125 scopus 로고
    • Models for the growth of solid tumors by diffusion
    • Greenspan, H. Models for the growth of solid tumors by diffusion. Stud. Appl. Math., 51: 317-340 (1972)
    • (1972) Stud. Appl. Math. , vol.51 , pp. 317-340
    • Greenspan, H.1
  • 15
    • 0017198676 scopus 로고
    • On the growth and stability of cell cultures and solid tumors
    • Greenspan, H. On the growth and stability of cell cultures and solid tumors. J. Theor. Biol., 56: 229-242 (1976)
    • (1976) J. Theor. Biol. , vol.56 , pp. 229-242
    • Greenspan, H.1
  • 16
    • 0027604157 scopus 로고
    • Cell migration in multicell spheroids: Swimming against the tide
    • McElwain, D., Pettet, G. Cell migration in multicell spheroids: swimming against the tide. Bull. Math. Biol. 55: 655-674 (1993)
    • (1993) Bull. Math. Biol. , vol.55 , pp. 655-674
    • McElwain, D.1    Pettet, G.2
  • 17
    • 0034977131 scopus 로고    scopus 로고
    • The migration of cells in multicell tumor spheroids
    • Pettet, G., Please, C., McElwain, M. The migration of cells in multicell tumor spheroids. Math. Biol., 63: 231-257 (2001)
    • (2001) Math. Biol. , vol.63 , pp. 231-257
    • Pettet, G.1    Please, C.2    McElwain, M.3
  • 19
    • 27844545167 scopus 로고    scopus 로고
    • A new mathematical model for vascular tumor growth
    • Sherrat, J., Chaplain, M. A new mathematical model for vascular tumor growth. Bull. Math. Biol., 61: 601-623 (1999)
    • (1999) Bull. Math. Biol. , vol.61 , pp. 601-623
    • Sherrat, J.1    Chaplain, M.2
  • 20
    • 0032838793 scopus 로고    scopus 로고
    • Modelling the internalization of labeled cells in tumor spheroids
    • Thompson, K., Byrne, H. Modelling the internalization of labeled cells in tumor spheroids. Bull. Math. Biol., 61: 601-623 (1999)
    • (1999) Bull. Math. Biol. , vol.61 , pp. 601-623
    • Thompson, K.1    Byrne, H.2
  • 21
    • 0031087466 scopus 로고    scopus 로고
    • Mathematical modeling of avascular-tumor growth
    • Ward, J., King, J. Mathematical modeling of avascular-tumor growth. IMA J. Math. Appl. Biol. Med., 14: 53-75 (1997)
    • (1997) IMA J. Math. Appl. Biol. Med. , vol.14 , pp. 53-75
    • Ward, J.1    King, J.2
  • 22
    • 0002484583 scopus 로고    scopus 로고
    • Mathematical modeling of avascular-tumor growth II: Modelling growth saturation
    • Ward, J., King, J. Mathematical modeling of avascular-tumor growth II: Modelling growth saturation. IMA J. Math. Appl. Med. Biol. 15: 1-42 (1998)
    • (1998) IMA J. Math. Appl. Med. Biol. , vol.15 , pp. 1-42
    • Ward, J.1    King, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.