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Free boundary value problems associated with the growth and development of multicellular spheroids. (English) Zbl 0906.92016
Summary: A generalized model for the growth of avascular tumours is presented. The formulation leads naturally to the incorporation of free boundaries which define the outer tumour surface explicitly and various inner surfaces implicitly. A combination of numerical simulations, asymptotic analysis and perturbation techniques is used to study the model and yields results, which agree well with experimentally-observed phenomena.
MSC:
92C50Medical applications of mathematical biology
35R35Free boundary problems for PDE
35Q80Appl. of PDE in areas other than physics (MSC2000)
92C15Developmental biology, pattern formation