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Zbl 0634.92002
Adam, John A.
A mathematical model of tumor growth. II. Effects of geometry and spatial nonuniformity on stability. (English)
[J] Math. Biosci. 86, 183-211 (1987). ISSN 0025-5564

Summary: A theoretical account of mitotic inhibition in one-, two-, and three- dimensional configurations is presented. Based on part I, ibid. 81, 229- 244 (1986; Zbl 0601.92007), the inhibitor production rate is taken to be nonuniform throughout the tissue, resulting in significant deviations from the prediction of uniform models. Geometry affects the stability of growth also. The analysis presented here represents a detailed study of the properties of highly nonuniform inhibition, from which information on intermediate inhibition models can be readily deduced. This information is used to compare such a model with experimental results in part III, see the following entry, Zbl 0634.92003.

MSC 2000:: *92C50 Medical appl. of mathematical biology
92D25 Population dynamics

Keywords: tumor growth; effects of geometry; spatial nonuniformity; stability; inhomogeneous diffusion equations; mitotic inhibition; three-dimensional configurations; inhibitor production rate; highly nonuniform inhibition

Citations: Zbl 0601.92007; Zbl 0634.92003

Cited in: Zbl 0634.92003

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Zentralblatt MATH Berlin [Germany]