A nonlinear structured population model of tumor growth with quiescence |
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| Authors: | M. Gyllenberg G. F. Webb |
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| Affiliation: | 1. Department of Applied Mathematics, Lule? University of Technology, S-95187, Lule?, Sweden
2. Department of Mathematics, Vanderbilt University, 37235, Nashville, TN, USA
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| Abstract: | A nonlinear structured cell population model of tumor growth is considered. The model distinguishes between two types of cells within the tumor: proliferating and quiescent. Within each class the behavior of individual cells depends on cell size, whereas the probabilities of becoming quiescent and returning to the proliferative cycle are in addition controlled by total tumor size. The asymptotic behavior of solutions of the full nonlinear model, as well as some linear special cases, is investigated using spectral theory of positive simigroup of operators. Supported in part by the National Science Foundation under Grant No. DMS-8722947 |
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| Keywords: | Nonlinear asynchronous exponential growth Positive semigroup Gompertzian growth |
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