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Long-time behavior of an angiogenesis model with flux at the tumor boundary

 

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Opened Access Long-time behavior of an angiogenesis model with flux at the tumor boundary
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Author: Cieslak, Tomasz
Morales Rodrigo, Cristian
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2013-12
Published in: Zeitschrift für Angewandte Mathematik und Physik, 64, 1625-1641.
Document type: Article
Abstract: This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model assumes a nonlinear flux at the tumor boundary and a nonlinear chemotactic response. It is proved that the choice of some key parameters influences the long-time behaviour of the system. More precisely, we show the convergence of solutions to different semi-trivial stationary states for different range of parameters.
Cite: Cieslak, T. y Morales Rodrigo, C. (2013). Long-time behavior of an angiogenesis model with flux at the tumor boundary. Zeitschrift für Angewandte Mathematik und Physik, 64, 1625-1641.
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Format: PDF

URI: http://hdl.handle.net/11441/45113

DOI: 10.1007/s00033-013-0302-8

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