Formation of stationary interfaces in the fast reaction limit

Fuente: arXiv
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Main Author: Tsukamoto, Yuki
Format: Preprint
Published: 2025
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_version_ 1866918055016136704
author Tsukamoto, Yuki
author_facet Tsukamoto, Yuki
contents We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat equation in the nonreactive region, while it remains zero elsewhere. The analysis is based on explicitly constructed barrier functions and a comparison argument adapted to systems with asymmetric reaction terms, which together provide control near the interface. As a result, the limiting behavior exhibits a stationary phase interface determined by the initial support of the reactive component.
format Preprint
id arxiv_https___arxiv_org_abs_2506_09716
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Formation of stationary interfaces in the fast reaction limit
Tsukamoto, Yuki
Analysis of PDEs
35K57, 35B25, 82C24
We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat equation in the nonreactive region, while it remains zero elsewhere. The analysis is based on explicitly constructed barrier functions and a comparison argument adapted to systems with asymmetric reaction terms, which together provide control near the interface. As a result, the limiting behavior exhibits a stationary phase interface determined by the initial support of the reactive component.
title Formation of stationary interfaces in the fast reaction limit
topic Analysis of PDEs
35K57, 35B25, 82C24
url https://arxiv.org/abs/2506.09716