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Analysis of a free boundary problem for avascular tumor growth with a periodic supply of nutrients

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  • In this paper we study a free boundary problem for the growth of avascular tumors. The establishment of the model is based on the diffusion of nutrient and mass conservation for the two process proliferation and apoptosis(cell death due to aging). It is assumed the supply of external nutrients is periodic. We mainly study the long time behavior of the solution, and prove that in the case $c$ is sufficiently small, the volume of the tumor cannot expand unlimitedly. It will either disappear or evolve to a positive periodic state.
    Mathematics Subject Classification: Primary: 35K57, 35K20; Secondary: 35B10.


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