# A well-posedness for the reaction diffusion equations of Belousov-Zhabotinsky reaction

## TL;DR

This paper proves the global existence and positivity of solutions to reaction-diffusion equations modeling the Belousov-Zhabotinsky reaction, using semigroup estimates, maximum principle, and invariant regions.

## Contribution

It establishes well-posedness and long-term behavior of solutions for the Keener-Tyson model in the whole space, which was previously unproven.

## Key findings

- Global existence of smooth positive solutions
- Solutions remain positive and bounded over time
- Analysis of long-term behavior of solutions

## Abstract

The time-global existence of unique smooth positive solutions to the reaction diffusion equations of the Keener-Tyson model for the Belousov-Zhabotinsky reaction in the whole space is established with bounded non-negative initial data. Deriving estimates of semigroups and time evolution operators, and applying the maximum principle, the unique existence and the positivity of solutions are ensured by construction of time-local solutions from certain successive approximation. Invariant regions and long time behavior of solutions are also discussed.