{"title":"自催化系统的行波&极限情况","authors":"Y. Qi","doi":"10.12732/CAA.V22I4.9","DOIUrl":null,"url":null,"abstract":"This article studies propagating wave of a reaction-diffusion system modeling auto-catalytic chemical reaction A+nB → (n+1)B involving two chemical species, a reactant A and an auto-catalyst B, whose diffusion coefficients, DA andDB , are unequal due to different molecular weights and/or sizes. We are investigating the extreme cases of D ≡ DB/DA ≪ 1 or D ≫ 1. We reformulate the traveling wave problem of general case to derive explicit bounds of speed for existence and non-existence. AMS Subject Classification: 34C20, 34C25, 92E20 Received: June 13, 2017 ; Accepted: October 31, 2018 ; Published: November 13, 2018. doi: 10.12732/caa.v22i4.9 Dynamic Publishers, Inc., Acad. Publishers, Ltd. http://www.acadsol.eu/caa","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"THE TRAVELING WAVE OF AUTO-CATALYTIC SYSTEMS – THE LIMITING CASES\",\"authors\":\"Y. Qi\",\"doi\":\"10.12732/CAA.V22I4.9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article studies propagating wave of a reaction-diffusion system modeling auto-catalytic chemical reaction A+nB → (n+1)B involving two chemical species, a reactant A and an auto-catalyst B, whose diffusion coefficients, DA andDB , are unequal due to different molecular weights and/or sizes. We are investigating the extreme cases of D ≡ DB/DA ≪ 1 or D ≫ 1. We reformulate the traveling wave problem of general case to derive explicit bounds of speed for existence and non-existence. AMS Subject Classification: 34C20, 34C25, 92E20 Received: June 13, 2017 ; Accepted: October 31, 2018 ; Published: November 13, 2018. doi: 10.12732/caa.v22i4.9 Dynamic Publishers, Inc., Acad. Publishers, Ltd. http://www.acadsol.eu/caa\",\"PeriodicalId\":92887,\"journal\":{\"name\":\"Communications in applied analysis\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in applied analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12732/CAA.V22I4.9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in applied analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12732/CAA.V22I4.9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
THE TRAVELING WAVE OF AUTO-CATALYTIC SYSTEMS – THE LIMITING CASES
This article studies propagating wave of a reaction-diffusion system modeling auto-catalytic chemical reaction A+nB → (n+1)B involving two chemical species, a reactant A and an auto-catalyst B, whose diffusion coefficients, DA andDB , are unequal due to different molecular weights and/or sizes. We are investigating the extreme cases of D ≡ DB/DA ≪ 1 or D ≫ 1. We reformulate the traveling wave problem of general case to derive explicit bounds of speed for existence and non-existence. AMS Subject Classification: 34C20, 34C25, 92E20 Received: June 13, 2017 ; Accepted: October 31, 2018 ; Published: November 13, 2018. doi: 10.12732/caa.v22i4.9 Dynamic Publishers, Inc., Acad. Publishers, Ltd. http://www.acadsol.eu/caa
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