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A nonlinear structured population model of tumor growth with quiescence. (English) Zbl 0744.92026
Summary: 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 semigroups of operators.

MSC:
92D25 Population dynamics (general)
47D03 Groups and semigroups of linear operators
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C50 Medical applications (general)
35B40 Asymptotic behavior of solutions to PDEs
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
47N60 Applications of operator theory in chemistry and life sciences
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