Year: 2025
Type: article
Abstract: We study a two-component reaction-diffusion system with asymmetric reaction terms, where only one component undergoes rapid interaction. 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.
DOI: 10.3934/eect.2025073
Author: Yuki Tsukamoto
Institution: Tokyo University of Science
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7090455184