# Traveling waves for degenerate diffusive equations on networks

## TL;DR

This paper investigates the existence of traveling wave solutions for degenerate diffusive equations on star graphs, with applications to traffic flow modeling at crossroads, providing algebraic conditions and detailed examples.

## Contribution

It establishes a necessary and sufficient algebraic condition for traveling wave existence on networks with degenerate diffusion, extending previous results to more general settings.

## Key findings

- Derived algebraic condition for traveling wave existence
- Analyzed quadratic and logarithmic flux functions
- Applied results to traffic flow models

## Abstract

In this paper we consider a scalar parabolic equation on a star graph; the model is quite general but what we have in mind is the description of traffic flows at a crossroad. In particular, we do not necessarily require the continuity of the unknown function at the node of the graph and, moreover, the diffusivity can be degenerate. Our main result concerns a necessary and sufficient algebraic condition for the existence of traveling waves in the graph. We also study in great detail some examples corresponding to quadratic and logarithmic flux functions, for different diffusivities, to which our results apply.