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Comparative analysis of continuum angiogenesis models. (English) Zbl 1460.92032
This paper is devoted to a comparison of two models of angiogenesis, i.e. the emergence of new blood vessels. Both models are based on partial differential equations. The first is a phenomenological “snail-trail” model, the second “coarse-grained” mean field type system is derived from microscopic considerations. The comparison is performed using analytic methods (perturbation theory) and numerical simulations.
MSC:
92C17 Cell movement (chemotaxis, etc.)
92C37 Cell biology
35B20 Perturbations in context of PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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