Constructing solutions for a kinetic model of angiogenesis in annular domains

TL;DR

This paper establishes the existence and stability of solutions for a complex kinetic model of angiogenesis in annular domains, combining advanced mathematical techniques to handle nonlocal boundary conditions and coupled diffusion equations.

Contribution

It introduces a rigorous mathematical framework proving existence and stability for a kinetic angiogenesis model with nonlocal boundary conditions in annular regions.

Findings

Proved existence of solutions for the model.

Established stability under certain conditions.

Developed new estimates for kinetic operators and heat kernels.

Abstract

We prove existence and stability of solutions for a model of angiogenesis set in an annular region. Branching, anastomosis and extension of blood vessel tips are 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. Our technique exploits 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.