{"title":"变量$t为负函数系统Cauchy问题的非局部可解性$","authors":"M. Dontsova","doi":"10.52737/18291163-2023.15.4-1-10","DOIUrl":null,"url":null,"abstract":"We obtain sufficient conditions for the existence and uniqueness of a local solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$ and show that the solution has the same $x$-smoothness as the initial function. We also obtain sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonlocal Solvability of the Cauchy Problem for a System with Negative Functions of the Variable $t$\",\"authors\":\"M. Dontsova\",\"doi\":\"10.52737/18291163-2023.15.4-1-10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We obtain sufficient conditions for the existence and uniqueness of a local solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$ and show that the solution has the same $x$-smoothness as the initial function. We also obtain sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$.\",\"PeriodicalId\":42323,\"journal\":{\"name\":\"Armenian Journal of Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-03-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Armenian Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.52737/18291163-2023.15.4-1-10\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Armenian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52737/18291163-2023.15.4-1-10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Nonlocal Solvability of the Cauchy Problem for a System with Negative Functions of the Variable $t$
We obtain sufficient conditions for the existence and uniqueness of a local solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$ and show that the solution has the same $x$-smoothness as the initial function. We also obtain sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$.
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