{"title":"常系数伪双曲型方程的解","authors":"Y. Kostikov, A. Romanenkov","doi":"10.46925//rdluz.39.12","DOIUrl":null,"url":null,"abstract":"Thepaperproposesthemethodofformingtheexactsolutionofthefirstinitialboundaryvalueproblemforone-dimensionallinearpseudohyperbolicequation with constant coefficients. Toobtainthesolutiontype, themodificationofpartitionmethod (Fourier method) is used, when the type of one of the solution functional factors is consideredto be known. Atthesametime, theinitialproblemisreducedto parameterized family of Cauchy problems for ordinary differential equations. Thepaperpresentsexplicitly calculated formulas, whichspecify the solution. The qualitative research of the solution properties has been conducted. Theconditionsforcoefficientsintheformofinequalitieshave been obtained that is indicative ofboundedness and variability of the solutions. Several examples confirming the results obtained have been considered.","PeriodicalId":42302,"journal":{"name":"Revista de la Universidad del Zulia","volume":"27 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On solution of pseudohyperbolic equation with constant coefficients\",\"authors\":\"Y. Kostikov, A. Romanenkov\",\"doi\":\"10.46925//rdluz.39.12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Thepaperproposesthemethodofformingtheexactsolutionofthefirstinitialboundaryvalueproblemforone-dimensionallinearpseudohyperbolicequation with constant coefficients. Toobtainthesolutiontype, themodificationofpartitionmethod (Fourier method) is used, when the type of one of the solution functional factors is consideredto be known. Atthesametime, theinitialproblemisreducedto parameterized family of Cauchy problems for ordinary differential equations. Thepaperpresentsexplicitly calculated formulas, whichspecify the solution. The qualitative research of the solution properties has been conducted. Theconditionsforcoefficientsintheformofinequalitieshave been obtained that is indicative ofboundedness and variability of the solutions. Several examples confirming the results obtained have been considered.\",\"PeriodicalId\":42302,\"journal\":{\"name\":\"Revista de la Universidad del Zulia\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista de la Universidad del Zulia\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46925//rdluz.39.12\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"SOCIAL SCIENCES, INTERDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista de la Universidad del Zulia","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46925//rdluz.39.12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"SOCIAL SCIENCES, INTERDISCIPLINARY","Score":null,"Total":0}
On solution of pseudohyperbolic equation with constant coefficients
Thepaperproposesthemethodofformingtheexactsolutionofthefirstinitialboundaryvalueproblemforone-dimensionallinearpseudohyperbolicequation with constant coefficients. Toobtainthesolutiontype, themodificationofpartitionmethod (Fourier method) is used, when the type of one of the solution functional factors is consideredto be known. Atthesametime, theinitialproblemisreducedto parameterized family of Cauchy problems for ordinary differential equations. Thepaperpresentsexplicitly calculated formulas, whichspecify the solution. The qualitative research of the solution properties has been conducted. Theconditionsforcoefficientsintheformofinequalitieshave been obtained that is indicative ofboundedness and variability of the solutions. Several examples confirming the results obtained have been considered.
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