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Constructing solutions for a kinetic model of angiogenesis in annular domains

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Carpio, Ana and Duro, Gema and Negreanu, Mihaela (2017) Constructing solutions for a kinetic model of angiogenesis in annular domains. Applied Mathematical Modelling, 45 . pp. 303-322. ISSN 0307-904X

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Official URL: https://doi.org/10.1016/j.apm.2016.12.028




Abstract

We present an iterative technique to construct stable solutions for an angiogenesis model set in an annular region. Branching, anastomosis and extension of blood vessel tips is described by an integrodifferential kinetic equation of Fokker-Planck type supplemented with nonlocal boundary conditions and coupled to a diffusion problem with Neumann boundary conditions through the force field created by the tumor induced angiogenic factor and the flux of vessel tips. Convergence proofs exploit balance equations, estimates of velocity decay and compactness results for kinetic operators, combined with gradient estimates of heat kernels for Neumann problems in non convex domains.


Item Type:Article
Uncontrolled Keywords:Angiogenesis, Integrodifferential model, Kinetic-diffusion equations, Fokker–Planck operator, Bounded domains, Nonlocal and Neumann boundary conditions
Subjects:Sciences > Mathematics > Differential equations
Sciences > Mathematics > Operations research
Medical sciences > Medicine > Cardiovascular system
ID Code:55835
Deposited On:18 Jun 2019 14:17
Last Modified:19 Jun 2019 07:51

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