Asymptotics of solutions in nA+nB->C reaction Diffusion systems

TL;DR

This paper investigates the long-term behavior of reaction-diffusion systems for the process nA + nB -> C, revealing complex dynamics on multiple scales for cases where n > 3.

Contribution

It extends previous studies by analyzing the asymptotic behavior of systems with n > 3, showing nontrivial dynamics on both reactive and diffusive scales.

Findings

For n > 3, solutions exhibit nontrivial behavior on reactive and diffusive scales.

The case n=1 shows behavior only on the reactive scale, contrasting with higher n.

Provides rigorous analysis of asymptotic behavior in complex reaction-diffusion systems.

Abstract

We analyze the long time behavior of initial value problems that model a process where particles of type A and B diffuse in some substratum and react according to $nA+nB\to C$. The case n=1 has been studied before; it presents nontrivial behavior on the reactive scale only. In this paper we discuss in detail the cases $n>3$, and prove that they show nontrivial behavior on the reactive and the diffusive length scale.