Vanishing interfaces in an asymmetric fast reaction limit

Abstract We study the fast reaction limit for a two-component reaction-diffusion system with asymmetric reaction terms, where only one component diffuses. For nonnegative and mutually segregated initial data, we prove that the initial interface vanishes instantaneously. More precisely, the diffusive component converges uniformly to the solution of the heat equation, while the non-diffusive component vanishes away from the initial time. The proof is based on explicit barriers and a comparison argument, and applies under both Dirichlet and Neumann boundary conditions.

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Publication Details

Journal
Nonlinear Differential Equations and Applications NoDEA
Published
2026-10-27
DOI
https://doi.org/10.1007/s00030-026-01288-y
Primary Topic
Nonlinear Partial Differential Equations
Type
article
Field-Weighted Citation Impact
0.00

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article

Vanishing interfaces in an asymmetric fast reaction limit

Yuki Tsukamoto
2 links
Nonlinear Differential Equations and Applications NoDEA
Nonlinear Partial Differential Equations
article

Vanishing interfaces in an asymmetric fast reaction limit

Yuki Tsukamoto
article en

Abstract

Abstract We study the fast reaction limit for a two-component reaction-diffusion system with asymmetric reaction terms, where only one component diffuses. For nonnegative and mutually segregated initial data, we prove that the initial interface vanishes instantaneously. More precisely, the diffusive component converges uniformly to the solution of the heat equation, while the non-diffusive component vanishes away from the initial time. The proof is based on explicit barriers and a comparison argument, and applies under both Dirichlet and Neumann boundary conditions.

Nonlinear Differential Equations and Applications NoDEAVol. 33(6)
Tokyo University of Science (JP)
Japan Society for the Promotion of Science
Openalex Percentile: Top 73%
Nonlinear Partial Differential Equations
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