Traveling waves with continuous profile for hyperbolic Keller-Segel equation

TL;DR

This paper investigates a hyperbolic PDE model for cell movement driven by repulsion, proving the existence of continuous-profile traveling waves and supporting findings with numerical simulations.

Contribution

It establishes the existence of continuous-profile traveling waves in a hyperbolic Keller-Segel model, extending previous sharp wave results.

Findings

Existence of continuous traveling wave solutions.

Numerical simulations illustrating wave profiles.

Extension of previous sharp wave results.

Abstract

This work describes a hyperbolic model for cell-cell repulsion with population dynamics. We consider the pressure produced by a population of cells to describe their motion. We assume that cells try to avoid crowded areas and prefer locally empty spaces far away from the carrying capacity. Here, our main goal is to prove the existence of traveling waves with continuous profiles. This article complements our previous results about sharp traveling waves. We conclude the paper with numerical simulations of the PDE problem, illustrating such a result.