# Existence of pulses for a reaction-diffusion system of blood coagulation

## TL;DR

This paper investigates the existence of pulse solutions in a reaction-diffusion model of blood coagulation, establishing a link between pulse existence and the positivity of wave speed using topological methods.

## Contribution

It demonstrates that pulse solutions exist if and only if the associated traveling wave speed is positive, providing a new criterion for pulse existence in blood coagulation models.

## Key findings

- Pulse solutions exist if and only if the wave speed is positive.
- The proof employs Leray-Schauder topological degree and a priori estimates.
- The study advances understanding of blood coagulation dynamics in reaction-diffusion systems.

## Abstract

The paper is devoted to the investigation of a reaction-diffusion system of equations describing the process of blood coagulation. Existence of pulses solutions, that is, positive stationary solutions with zero limit at infinity is studied. It is shown that such solutions exist if and only if the speed of the travelling wave described by the same system is positive. The proof is based on the Leray-Schauder method using topological degree for elliptic problems in unbounded domains and a priori estimates of solutions in some appropriate weighted spaces.