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July  2007, 8(1): 45-60. doi: 10.3934/dcdsb.2007.8.45

An age and spatially structured model of tumor invasion with haptotaxis

Janet Dyson 1, , Eva Sánchez 2, , Rosanna Villella-Bressan 3, and  Glenn F. Webb 4,

1. 

Department of Mathematics, Mansfield College, Oxford University, Oxford, England
2. 

Depto. de Matemática Aplicada, E.T.S.I. Industriales, c. José Gutiérrez Abascal, 2, 28006 Madrid
3. 

Dipartimento di Matematica Pura e Applicata, Universita' di Padova, Padua
4. 

Mathematics Department, Vanderbilt University, Nashville, TN 37240, United States

Received  November 2006 Revised  December 2006 Published  April 2007

A model of tumor growth into surrounding tissue is analyzed. The model consists of a system of nonlinear partial differential equations for the populations of tumor cells, extracellular matrix macromolecules, oxygen concentration, and extracellular matrix degradative enzyme concentration. The spatial growth of the tumor involves the directed movement of tumor cells toward the extracellular matrix through haptotaxis. Cell age is used to track progression of cells through the cell cycle. The existence of unique global solutions is proved using the theory of fractional powers of analytic semigroup generators.
Keywords: haptotaxis, tumor model., Semigroups of operators, diffusion.
Mathematics Subject Classification: Primary:92B05,92D25,47D03,47H20; Secondary: 35M1.
Citation: Janet Dyson, Eva Sánchez, Rosanna Villella-Bressan, Glenn F. Webb. An age and spatially structured model of tumor invasion with haptotaxis. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 45-60. doi: 10.3934/dcdsb.2007.8.45
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