{"title":"关于波动方程和卷积的注解","authors":"A. Kılıçman, H. Eltayeb","doi":"10.1155/2007/49251","DOIUrl":null,"url":null,"abstract":"We study the first-order nonhomogenous wave equation. We extend the convolution theorem into a general case with a double convolution as the nonhomogenous term. The uniqueness and continuity of the solution are proved and we provide some examples in order to validate our results.","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"2007 1","pages":"1-13"},"PeriodicalIF":0.0000,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2007/49251","citationCount":"1","resultStr":"{\"title\":\"A Note on Wave Equation and Convolutions\",\"authors\":\"A. Kılıçman, H. Eltayeb\",\"doi\":\"10.1155/2007/49251\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the first-order nonhomogenous wave equation. We extend the convolution theorem into a general case with a double convolution as the nonhomogenous term. The uniqueness and continuity of the solution are proved and we provide some examples in order to validate our results.\",\"PeriodicalId\":30100,\"journal\":{\"name\":\"Differential Equations and Nonlinear Mechanics\",\"volume\":\"2007 1\",\"pages\":\"1-13\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1155/2007/49251\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations and Nonlinear Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2007/49251\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations and Nonlinear Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2007/49251","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We study the first-order nonhomogenous wave equation. We extend the convolution theorem into a general case with a double convolution as the nonhomogenous term. The uniqueness and continuity of the solution are proved and we provide some examples in order to validate our results.
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