Existence of radial stationary solutions for a system in combustion theory

TL;DR

This paper proves the existence of two radially symmetric stationary solutions for a simplified nonlinear elliptic system modeling combustion with radiation losses, using degree theory.

Contribution

It introduces a new simplified model for flame balls with radiation losses and demonstrates the existence of multiple solutions through degree theory.

Findings

Existence of two radially symmetric solutions established.

Model simplifies radiation term and approximates Arrhenius law.

Uses degree theory to prove solution existence.

Abstract

In this paper, we construct radially symmetric solutions of a nonlinear noncooperative elliptic system derived from a model for flame balls with radiation losses. This model is based on a one step kinetic reaction and our system is obtained by approximating the standard Arrehnius law by an ignition nonlinearity, and by simplifying the term that models radiation. We prove the existence of 2 solutions using degree theory.