Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors

Interfaces and Free Boundaries

Volumn 7, Issue 2, 2005, Pages 147-159

  Cui, Shangbin ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

Existence; Free boundary problem; Global solution; Tumor growth

Indexed keywords

EID: 22544467766     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/118     Document Type: Article

References (21)

1. ADAM, J. & BELLOMO, N. A Survey of Models for Tumor-Immune System Dynamics, Birkhäuser, Boston (1997). Zbl 0874.92020
2. BAZALIY, B. & FRIEDMAN, A. A free boundary problem for an elliptic-parabolic system: application to a model of tumor growth, Comm. Partial Differential Equations 28 (2003), 517-560. Zbl 1031.35151 MR 1976462
3. BAZALIY, B. & FRIEDMAN, A. Global existence and stability for an elliptic-parabolic free boundary problem: application to a model of tumor growth, Indiana Univ. Math. J. 52 (2003), 1265-1304. MR 2010327
4. BYRNE, H. M. & CHAPLAIN, M. A. J. Growth of nonnecrotic tumors in the presence and absence of inhibitors, Math. Biosci. 130 (1995), 151-181. Zbl 0836.92011
5. BYRNE, H. M. & CHAPLAIN, M. A. J. Growth of necrotic tumors in the presence and absence of inhibitors, Math. Biosci. 135 (1996), 187-216. Zbl 0856.92010
6. BYRNE, H. M. & CHAPLAIN, M. A. J. Free boundary value problems associated with the growth and development of multicellular spheroids, European J. Appl. Math. 8 (1997), 639-658. Zbl 0906.92016 MR 1608619
7. CUI, S. Analysis of a mathematical model for the growth of tumors under the action of external inhibitors, J. Math. Biol. 44 (2002), 395-426. Zbl 1019.92017 MR 1908130
8. CUI, S. & FRIEDMAN, A. Analysis of a mathematical model of the effect of inhibitors on the growth of tumors, Math. Biosci. 164 (2000), 103-137. Zbl 0998.92022 MR 1751267
9. CUI, S. & FRIEDMAN, A. Analysis of a mathematical model of the growth of necrotic tumors, J. Math. Anal. Appl. 255 (2001), 636-677. Zbl 0984.35169 MR 1815805
10. CUI, S. & FRIEDMAN, A. A hyperbolic free boundary problem modeling tumor growth, Interfaces Free Bound. 5 (2003), 159-181. Zbl 1040.35143 MR 1980470
11. GUI, 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 (2003), 3537-3590. Zbl 1036.34018 MR 1990162
12. FRIEDMAN, A. & REITICH, F. Analysis of a mathematical model for the growth of tumors, J. Math. Biol. 38 (1999), 262-284. Zbl 0944.92018 MR 1684873
13. FRIEDMAN, A. & REITICH, F. Symmetry-breaking bifurcation of analytic solutions to a free boundary problem: An application to a model of tumor growth, Trans. Amer. Math. Soc. 353 (2000), 1587-1634. Zbl 0983.35019 MR 1806728
14. FRIEDMAN, A. & REITICH, F. On the existence of spatially patterned dormant malignancies in the model for the growth of non-necrotic vascular tumor, Math. Models Methods Appl. Sci. 11 (2001), 601-625. Zbl 1013.92024 MR 1832995
15. GREENSPAN, H. P. Models for the growth of a solid tumor by diffusion, Stud. Appl. Math. 52 (1972), 317-340. Zbl 0257.92001
16. GREENSPAN, H. P. On the growth and stability of cell cultures and solid tumors, J. Theor. Biol. 56 (1976), 229-242. MR 0429164
17. JONES, A. F., BYRNE, H. M., GIBSON, J. S., & DOLD, J. W. A mathematical model of the stress induced during avascular tumor growth, J. Math. Biol. 40 (2000), 473-499. Zbl 0964.92025 MR 1770937
18. PETTET, G., PLEASE, C. P., TINDALL, M. J., & MCELWAIN, D. The migration of cells in multicell tumor spheroids, Bull. Math. Biol. 63 (2001), 231-257.
19. SUTHERLAND, R. M. Cell and environmental interactions in tumor microregions: The multicell spheroid model, Science 240 (1988), 177-184.
20. WARD, J. P. & KING, J. R. Mathematical modelling of avascular-tumour growth, IMA J. Math. Appl. Med. Biol. 14 (1997), 39-69. Zbl 0866.92011
21. WARD, J. P. & KING, J. R. Mathematical modelling of avascular-tumour growth II: Modelling growth saturation, IMA J. Math. Appl. Med. Biol. 16 (1999), 171-211. Zbl 0943.92019