Well-posedness for a model of individual clustering

TL;DR

This paper investigates the mathematical well-posedness of a model describing individual clustering, establishing local existence and uniqueness of solutions, and analyzing global behavior and steady states for specific reproduction rates.

Contribution

It proves local existence and uniqueness of solutions for the model and demonstrates global existence and convergence to steady states for certain reproduction rates.

Findings

Proves local existence and uniqueness of solutions.

Establishes global existence for specific reproduction rates in one dimension.

Shows convergence to steady states under certain conditions.

Abstract

We study the well-posedness of a model of individual clustering. Given p > N \geq 1 and an initial condition in W 1,p (\Omega), the local existence and uniqueness of a strong solution is proved. We next consider two specific reproduction rates and show global existence if N = 1, as well as, the convergence to steady states for one of these rates.