English

Vanishing interfaces in an asymmetric fast reaction limit

Analysis of PDEs 2026-04-28 v1

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.

Keywords

Cite

@article{arxiv.2604.24318,
  title  = {Vanishing interfaces in an asymmetric fast reaction limit},
  author = {Yuki Tsukamoto},
  journal= {arXiv preprint arXiv:2604.24318},
  year   = {2026}
}

Comments

20 pages

R2 v1 2026-07-01T12:36:55.437Z