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VOL. 64 | 2015 Allen–Cahn equation as a long-time modulation to a reaction-diffusion system
Thomas Bellsky

Editor(s) Shin-Ichiro Ei, Shuichi Kawashima, Masato Kimura, Tetsu Mizumachi

## Abstract

We examine a two-component reaction-diffusion system on the real axis with quadratic nonlinearity. Using semigroup estimates, we obtain a solution to our nonlinear system for long-time. For appropriate initial data, we show that a slowly-varying, scaled solution of the Allen–Cahn equation will estimate the solution of our nonlinear system for long-time. We additionally extend this work to $\mathbb{R}^d$.

## Information

Published: 1 January 2015
First available in Project Euclid: 30 October 2018

zbMATH: 1336.35196
MathSciNet: MR3381302

Digital Object Identifier: 10.2969/aspm/06410359

Subjects:
Primary: 35B35, 35B40, 35K57