dorsal/arxiv
View SchemaAsymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system
| Authors | Xiao-Biao Lin |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9403002 |
| URL | https://arxiv.org/abs/patt-sol/9403002 |
Abstract
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order in $\epsilon$. The formal solution shows that there is an invariant manifold of wave-front-like solutions that attracts other nearby solutions. With an additional assumption on the sign of the wave speed, the wave-front-like solutions converge slowly to stable stationary solutions on that manifold.
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"date_created": "2026-03-02T18:00:28.848000Z",
"date_modified": "2026-03-02T18:00:28.848000Z",
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"abstract": "For a singularly perturbed system of reaction--diffusion equations, assuming\nthat the 0th order solutions in regular and singular regions are all stable, we\nconstruct matched asymptotic expansions for formal solutions to any desired\norder in $\\epsilon$. The formal solution shows that there is an invariant\nmanifold of wave-front-like solutions that attracts other nearby solutions.\nWith an additional assumption on the sign of the wave speed, the\nwave-front-like solutions converge slowly to stable stationary solutions on\nthat manifold.",
"arxiv_id": "patt-sol/9403002",
"authors": [
"Xiao-Biao Lin"
],
"categories": [
"patt-sol",
"chao-dyn",
"nlin.CD",
"nlin.PS"
],
"title": "Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system",
"url": "https://arxiv.org/abs/patt-sol/9403002"
},
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"variant": "snapshot-2026-03-01",
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