{"title":"Internal Transition Layer Structure in the Reaction–Diffusion Problem for the Case of a Balanced Reaction with a Weak Discontinuity","authors":"E. I. Nikulin, V. T. Volkov, D. A. Karmanov","doi":"10.1134/s0012266124010063","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> For a singularly perturbed reaction–diffusion equation, we study the structure of the\ninternal transition layer in the case of a balanced reaction with a weak discontinuity. The\nexistence of solutions with an internal transition layer (contrast structures) is proved, the question\nof their stability is investigated, and asymptotic approximations to solutions of this type are\nobtained. It is shown that in the case of reaction balance, the presence of even a weak\n(asymptotically small) reaction discontinuity can lead to the formation of contrast structures of\nfinite size, both stable and unstable.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124010063","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
For a singularly perturbed reaction–diffusion equation, we study the structure of the
internal transition layer in the case of a balanced reaction with a weak discontinuity. The
existence of solutions with an internal transition layer (contrast structures) is proved, the question
of their stability is investigated, and asymptotic approximations to solutions of this type are
obtained. It is shown that in the case of reaction balance, the presence of even a weak
(asymptotically small) reaction discontinuity can lead to the formation of contrast structures of
finite size, both stable and unstable.
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