{"title":"Klein-Gordon方程非平稳边值问题的边界积分方程","authors":"Bayegizova Aigulim, Dadayeva Assiyat","doi":"10.5772/intechopen.91693","DOIUrl":null,"url":null,"abstract":"The non-stationary boundary value problems for Klein-Gordon equation with Dirichlet or Neumann conditions on the boundary of the domain of definition are considered; a uniqueness of boundary value problems is proved. Based on the generalized functions method, boundary integral equations method is developed to solve the posed problems in strengths of shock waves. Dynamic analogs of Green’s formulas for solutions in the space of generalized functions are obtained and their regular integral representations are constructed in 2D and 3D over space cases. The singular boundary integral equations are obtained which resolve these tasks.","PeriodicalId":383521,"journal":{"name":"Mathematical Theorems - Boundary Value Problems and Approximations","volume":"47 10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Boundary Integral Equations of no Stationary Boundary Value Problems for the Klein-Gordon Equation\",\"authors\":\"Bayegizova Aigulim, Dadayeva Assiyat\",\"doi\":\"10.5772/intechopen.91693\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The non-stationary boundary value problems for Klein-Gordon equation with Dirichlet or Neumann conditions on the boundary of the domain of definition are considered; a uniqueness of boundary value problems is proved. Based on the generalized functions method, boundary integral equations method is developed to solve the posed problems in strengths of shock waves. Dynamic analogs of Green’s formulas for solutions in the space of generalized functions are obtained and their regular integral representations are constructed in 2D and 3D over space cases. The singular boundary integral equations are obtained which resolve these tasks.\",\"PeriodicalId\":383521,\"journal\":{\"name\":\"Mathematical Theorems - Boundary Value Problems and Approximations\",\"volume\":\"47 10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-04-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Theorems - Boundary Value Problems and Approximations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5772/intechopen.91693\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Theorems - Boundary Value Problems and Approximations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5772/intechopen.91693","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Boundary Integral Equations of no Stationary Boundary Value Problems for the Klein-Gordon Equation
The non-stationary boundary value problems for Klein-Gordon equation with Dirichlet or Neumann conditions on the boundary of the domain of definition are considered; a uniqueness of boundary value problems is proved. Based on the generalized functions method, boundary integral equations method is developed to solve the posed problems in strengths of shock waves. Dynamic analogs of Green’s formulas for solutions in the space of generalized functions are obtained and their regular integral representations are constructed in 2D and 3D over space cases. The singular boundary integral equations are obtained which resolve these tasks.
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