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An elliptic-hyperbolic free boundary problem modelling cancer therapy. (English) Zbl 1105.35149
The paper deals with a model for the evolution of a spheroidal tumor under the combined action of nutrient and of a drug. The volume is filled by living cells and dead cells, keeping constant size (there is no interstitial liquid and dead cells do not degrade). All components move with the same velocity. For the diffusion of the nutrient and of the drug the quasi-steady approximation is taken. Existence is proved using a fixed point argument. The result is global in time and under certain hypotheses the external radius of the spheroid is shown to tend to a finite limit. For suitable assumptions on the parameters the final state is characterized by the absence of living cells. The case of unbounded growth is also considered.

MSC:
35R35 Free boundary problems for PDEs
92C50 Medical applications (general)
92C37 Cell biology
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