Constructing solutions for a kinetic model of angiogenesis in annular domains
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 a...
| Authors: | ; ; |
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| Format: | Article |
| Publication date: | 2017 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/18799 |
| Online Access: | https://hdl.handle.net/20.500.14352/18799 |
| Access Level: | Open access |
| Keyword: | 519.8 Angiogenesis Integrodifferential model Kinetic-diffusion equations Fokker–Planck operator Bounded domains Nonlocal and Neumann boundary conditions Ecuaciones diferenciales Investigación operativa (Matemáticas) Sistema cardiovascular 1202.07 Ecuaciones en Diferencias 1207 Investigación Operativa 2411.03 Fisiología Cardiovascular |
| Summary: | 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. |
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