Well posedness of an angiogenesis related integrodifferential diffusion model

TL;DR

This paper establishes the mathematical well-posedness, including existence and uniqueness, of a nonlocal integrodifferential diffusion model pertinent to angiogenesis, using fundamental solutions, comparison principles, and integral inequalities.

Contribution

It provides the first rigorous proof of well-posedness for a nonlocal angiogenesis-related diffusion model, ensuring stability and convergence of solutions.

Findings

Existence of nonnegative solutions is proven.

Uniqueness of solutions is established.

Stability bounds for the model are derived.

Abstract

We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded coefficients allow us to generate sequences of approximate solutions. Comparison principles and integral equations provide uniform bounds ensuring some convergence properties for iterative schemes and providing stability bounds. Uniqueness follows from chained integral inequalities.