-
1
-
-
0022799748
-
A simplified mathematical model of tumor growth
-
Adam J.A. A simplified mathematical model of tumor growth. Math. Biosci. 81 (1986) 229-244
-
(1986)
Math. Biosci.
, vol.81
, pp. 229-244
-
-
Adam, J.A.1
-
2
-
-
0023475416
-
A mathematical model of tumour growth, II. Effects of geometry and spatial nonuniformity on stability
-
Adam J.A. A mathematical model of tumour growth, II. Effects of geometry and spatial nonuniformity on stability. Math. Biosci. 86 (1987) 213
-
(1987)
Math. Biosci.
, vol.86
, pp. 213
-
-
Adam, J.A.1
-
3
-
-
0023475416
-
A mathematical model of tumour growth, III. Comparison with experiment
-
Adam J.A. A mathematical model of tumour growth, III. Comparison with experiment. Math. Biosci. 86 (1987) 213
-
(1987)
Math. Biosci.
, vol.86
, pp. 213
-
-
Adam, J.A.1
-
4
-
-
0030822132
-
The effect of time delays on the dynamics of avascular tumour growth
-
Byrne H.M. The effect of time delays on the dynamics of avascular tumour growth. Math. Biosci. 144 (1997) 83-117
-
(1997)
Math. Biosci.
, vol.144
, pp. 83-117
-
-
Byrne, H.M.1
-
5
-
-
0028790729
-
Growth of non-necrotic tumors in the presence and absence of inhibitors
-
Byrne H.M., and Chaplain M.A.J. Growth of non-necrotic tumors in the presence and absence of inhibitors. Math. Biosci. 130 (1995) 151
-
(1995)
Math. Biosci.
, vol.130
, pp. 151
-
-
Byrne, H.M.1
Chaplain, M.A.J.2
-
6
-
-
0030586186
-
Growth of necrotic tumours in the presence and absence of inhibitors
-
Byrne H.M., and Chaplain M.A.J. Growth of necrotic tumours in the presence and absence of inhibitors. Math. Biosci. 135 (1996) 187
-
(1996)
Math. Biosci.
, vol.135
, pp. 187
-
-
Byrne, H.M.1
Chaplain, M.A.J.2
-
7
-
-
0003169993
-
Necrosis and apoptosis: Distinct cell loss mechanisms in a mathematical model of avascular tumor growth
-
Byrne H.M., and Chaplain M.A.J. Necrosis and apoptosis: Distinct cell loss mechanisms in a mathematical model of avascular tumor growth. J. Theor. Med. 1 (1998) 223
-
(1998)
J. Theor. Med.
, vol.1
, pp. 223
-
-
Byrne, H.M.1
Chaplain, M.A.J.2
-
8
-
-
0031320752
-
Free boundary value problems associated with the growth and development of multicellular spheroids
-
Byrne H.M., and Chaplain M.A.J. Free boundary value problems associated with the growth and development of multicellular spheroids. Eur. J. Appl. Math. 8 (1997) 639
-
(1997)
Eur. J. Appl. Math.
, vol.8
, pp. 639
-
-
Byrne, H.M.1
Chaplain, M.A.J.2
-
9
-
-
0030431867
-
Modelling the role of cell-cell adhesion in the growth and development of carcinomas
-
Byrne H.M., and Chaplain M.A.J. Modelling the role of cell-cell adhesion in the growth and development of carcinomas. Math. Comput. Modelling 24 (1996) 1-17
-
(1996)
Math. Comput. Modelling
, vol.24
, pp. 1-17
-
-
Byrne, H.M.1
Chaplain, M.A.J.2
-
10
-
-
0026568374
-
Variation in tumour cell growth rates and metabolism with oxygen-concentration, glucose-concentration and extracellular pH
-
Cascari J., Dotirchos S., and Sutherland R. Variation in tumour cell growth rates and metabolism with oxygen-concentration, glucose-concentration and extracellular pH. J. Cell. Physiol. 151 (1992) 386-394
-
(1992)
J. Cell. Physiol.
, vol.151
, pp. 386-394
-
-
Cascari, J.1
Dotirchos, S.2
Sutherland, R.3
-
11
-
-
0027437155
-
Modelling the growth of solid tumours and incorporating a method for their classification using nonlinear elasticity theory
-
Chaplain M.A.J., and Sleeman B.D. Modelling the growth of solid tumours and incorporating a method for their classification using nonlinear elasticity theory. J. Math. Biol. 31 (1992) 431-473
-
(1992)
J. Math. Biol.
, vol.31
, pp. 431-473
-
-
Chaplain, M.A.J.1
Sleeman, B.D.2
-
12
-
-
0027437155
-
Modelling the growth of solid tumors and incorporating a method for their classification using nonlinear elasticity theory
-
Chaplain M.A.J., and Sleeman B.D. Modelling the growth of solid tumors and incorporating a method for their classification using nonlinear elasticity theory. J. Math. Biol. 31 (1993) 431-473
-
(1993)
J. Math. Biol.
, vol.31
, pp. 431-473
-
-
Chaplain, M.A.J.1
Sleeman, B.D.2
-
13
-
-
3142764638
-
A free boundary problem for an elliptic-hyperbolic system: An application to tumor growth
-
Chen X., and Freidman A. A free boundary problem for an elliptic-hyperbolic system: An application to tumor growth. SIAM J. Math. Anal. 35 4 (2003) 974-986
-
(2003)
SIAM J. Math. Anal.
, vol.35
, Issue.4
, pp. 974-986
-
-
Chen, X.1
Freidman, A.2
-
14
-
-
0042363716
-
A free boundary problem for a singular system of differential equations: An application to a model of tumor growth
-
Cui S., and Freidman 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 9 (2003) 3537-3590
-
(2003)
Trans. Amer. Math. Soc.
, vol.355
, Issue.9
, pp. 3537-3590
-
-
Cui, S.1
Freidman, A.2
-
15
-
-
0347504530
-
Mathematical modelling of comedo ductal carcinoma in situ of the breast
-
Franks S.J., Byrne H.M., et al. Mathematical modelling of comedo ductal carcinoma in situ of the breast. Math. Medicine Biol. 20 (2003) 277-308
-
(2003)
Math. Medicine Biol.
, vol.20
, pp. 277-308
-
-
Franks, S.J.1
Byrne, H.M.2
-
16
-
-
0346031985
-
Modelling the early growth of ductal carcinoma in situ of the breast
-
Franks S.J., Byrne H.M., et al. Modelling the early growth of ductal carcinoma in situ of the breast. J. Math. Biol. 47 (2003) 424-452
-
(2003)
J. Math. Biol.
, vol.47
, pp. 424-452
-
-
Franks, S.J.1
Byrne, H.M.2
-
17
-
-
9644281465
-
Biological inferences from a mathematical model of comedo ductal carcinoma in situ of the breast
-
Franks S.J., Byrne H.M., et al. Biological inferences from a mathematical model of comedo ductal carcinoma in situ of the breast. J. Theoret. Biol. 232 4 (2005) 523-543
-
(2005)
J. Theoret. Biol.
, vol.232
, Issue.4
, pp. 523-543
-
-
Franks, S.J.1
Byrne, H.M.2
-
18
-
-
1042279440
-
A hierrchy of cancer models and their mathematical challenges
-
Friedman A. A hierrchy of cancer models and their mathematical challenges. Discrete Contin. Dyn. Syst. Ser. B 4 1 (2004) 147-159
-
(2004)
Discrete Contin. Dyn. Syst. Ser. B
, vol.4
, Issue.1
, pp. 147-159
-
-
Friedman, A.1
-
19
-
-
0033094895
-
Analysis of a mathematical model for the growth of tumours
-
Friedman A., and Reitich F. Analysis of a mathematical model for the growth of tumours. J. Math. Biol. 38 (1999) 262-284
-
(1999)
J. Math. Biol.
, vol.38
, pp. 262-284
-
-
Friedman, A.1
Reitich, F.2
-
20
-
-
0242588180
-
Symmetry-breaking bifurcation of analytic solutions to free boundary problems: An application to a model of tumor growth
-
Friedman A., and 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 (2000) 1587-1634
-
(2000)
Trans. Amer. Math. Soc.
, vol.353
, pp. 1587-1634
-
-
Friedman, A.1
Reitich, F.2
-
21
-
-
58049153053
-
Models for the growth of a solid tumor by diffusion
-
Greenspan H.P. Models for the growth of a solid tumor by diffusion. Nature 379 (1996) 88-91
-
(1996)
Nature
, vol.379
, pp. 88-91
-
-
Greenspan, H.P.1
-
22
-
-
0016373920
-
On the self-inhibited growth of cell cultures
-
Greenspan H.P. On the self-inhibited growth of cell cultures. Growth 38 (1974) 81-95
-
(1974)
Growth
, vol.38
, pp. 81-95
-
-
Greenspan, H.P.1
-
23
-
-
0017198676
-
On the growth and stability of cell cultures and solid tumors
-
Greenspan H.P. On the growth and stability of cell cultures and solid tumors. J. Theoret. Biol. 56 (1976) 229-242
-
(1976)
J. Theoret. Biol.
, vol.56
, pp. 229-242
-
-
Greenspan, H.P.1
-
24
-
-
0023848708
-
Joint oxygen-glucose deprivation as the cause of necrosis in a tumor analogue
-
Hlatky L., Suchs R., and Alpen E. Joint oxygen-glucose deprivation as the cause of necrosis in a tumor analogue. J. Cell. Physiol. 134 (1988) 167-178
-
(1988)
J. Cell. Physiol.
, vol.134
, pp. 167-178
-
-
Hlatky, L.1
Suchs, R.2
Alpen, E.3
-
26
-
-
0017185248
-
Oxygen diffusion in a spheroid cell with non-linear uptake kinetics
-
Lin S. Oxygen diffusion in a spheroid cell with non-linear uptake kinetics. J. Theoret. Biol. 60 (1976) 449-457
-
(1976)
J. Theoret. Biol.
, vol.60
, pp. 449-457
-
-
Lin, S.1
-
27
-
-
0020464689
-
The glucose distribution in 9L, rat brain multicell tumor spheroids and its effect on cell necrosis
-
Li C. The glucose distribution in 9L, rat brain multicell tumor spheroids and its effect on cell necrosis. Cancer 50 (1982) 2066-2073
-
(1982)
Cancer
, vol.50
, pp. 2066-2073
-
-
Li, C.1
-
28
-
-
0017878760
-
Areexamination of oxygen diffusion in a spheroid cell with Michaelis-Mentor oxygen uptake kinetics
-
McElwain D. Areexamination of oxygen diffusion in a spheroid cell with Michaelis-Mentor oxygen uptake kinetics. J. Theoret. Biol. 71 (1978) 255-267
-
(1978)
J. Theoret. Biol.
, vol.71
, pp. 255-267
-
-
McElwain, D.1
-
30
-
-
0031087466
-
Mathematical modelling of avasculartumour growth
-
Ward J.P., and King J.R. Mathematical modelling of avasculartumour growth. IMA J. Math. Appl. Med. Biol. 14 (1997) 39-69
-
(1997)
IMA J. Math. Appl. Med. Biol.
, vol.14
, pp. 39-69
-
-
Ward, J.P.1
King, J.R.2
-
31
-
-
0033028947
-
Mathematical modelling of avasculartumour growth II: Modelling growth saturation
-
Ward J.P., and King J.R. Mathematical modelling of avasculartumour growth II: Modelling growth saturation. IMA J. Math. Appl. Med. Biol. 16 (1999) 171-211
-
(1999)
IMA J. Math. Appl. Med. Biol.
, vol.16
, pp. 171-211
-
-
Ward, J.P.1
King, J.R.2
-
32
-
-
1042279436
-
A free boundary problem model of ductal carcinoma in situ
-
Xu Y. A free boundary problem model of ductal carcinoma in situ. Discrete Contin. Dyn. Syst. Ser. B 4 1 (2004) 337-348
-
(2004)
Discrete Contin. Dyn. Syst. Ser. B
, vol.4
, Issue.1
, pp. 337-348
-
-
Xu, Y.1
-
33
-
-
58049172803
-
A mathematical model of ductal carcinoma in situ and its characteristic stationary solutions
-
Begehr H., et al. (Ed), World Scientific
-
Xu Y. A mathematical model of ductal carcinoma in situ and its characteristic stationary solutions. In: Begehr H., et al. (Ed). Advances in Analysis (2005), World Scientific
-
(2005)
Advances in Analysis
-
-
Xu, Y.1
-
34
-
-
58049172187
-
A free boundary problem of diffusion equation with integral condition
-
Xu Y. A free boundary problem of diffusion equation with integral condition. Appl. Anal. 85 9 (2006) 1143-1152
-
(2006)
Appl. Anal.
, vol.85
, Issue.9
, pp. 1143-1152
-
-
Xu, Y.1
-
35
-
-
58049145791
-
A free boundary problem of parabolic complex equation
-
Xu Y. A free boundary problem of parabolic complex equation. Complex Var. Elliptic Equ. 51 8-11 (2006) 945-951
-
(2006)
Complex Var. Elliptic Equ.
, vol.51
, Issue.8-11
, pp. 945-951
-
-
Xu, Y.1
-
36
-
-
58049142100
-
An inverse problem for the free boundary model of ductal carcinoma in situ
-
Begehr H., and Nicolosi F. (Eds), World Science Publisher
-
Xu Y. An inverse problem for the free boundary model of ductal carcinoma in situ. In: Begehr H., and Nicolosi F. (Eds). More Progresses in Analysis (2008), World Science Publisher 1429-1438
-
(2008)
More Progresses in Analysis
, pp. 1429-1438
-
-
Xu, Y.1
|