{"title":"线性耗散波动方程的拉普拉斯变换精确解析解","authors":"M. Jamil, R. Khan, K. Shah","doi":"10.52280/pujm.2021.530605","DOIUrl":null,"url":null,"abstract":"A wave phenomena evolved day after day, as various concepts\nregarding waves appeared with the passage of time. These phenomena\nare generally modelled mathematically by partial differential equations\n(PDEs). In this research, we investigate the exact analytical solutions\nof one and two dimensional linear dissipative wave equations which are\nmodelled by second order PDEs with use of some initial and boundary\nconditions. We use double Laplace transform (DLT) and triple Laplace\ntransform (TLT) methods to determine these exact analytical solutions.\nWe provide examples with figures to test effectiveness of this scheme of\nLaplace transform","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Exact Analytical Solutions of Linear Dissipative Wave Equations via Laplace\\nTransform Method\",\"authors\":\"M. Jamil, R. Khan, K. Shah\",\"doi\":\"10.52280/pujm.2021.530605\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A wave phenomena evolved day after day, as various concepts\\nregarding waves appeared with the passage of time. These phenomena\\nare generally modelled mathematically by partial differential equations\\n(PDEs). In this research, we investigate the exact analytical solutions\\nof one and two dimensional linear dissipative wave equations which are\\nmodelled by second order PDEs with use of some initial and boundary\\nconditions. We use double Laplace transform (DLT) and triple Laplace\\ntransform (TLT) methods to determine these exact analytical solutions.\\nWe provide examples with figures to test effectiveness of this scheme of\\nLaplace transform\",\"PeriodicalId\":205373,\"journal\":{\"name\":\"Punjab University Journal of Mathematics\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Punjab University Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.52280/pujm.2021.530605\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Punjab University Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52280/pujm.2021.530605","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Exact Analytical Solutions of Linear Dissipative Wave Equations via Laplace
Transform Method
A wave phenomena evolved day after day, as various concepts
regarding waves appeared with the passage of time. These phenomena
are generally modelled mathematically by partial differential equations
(PDEs). In this research, we investigate the exact analytical solutions
of one and two dimensional linear dissipative wave equations which are
modelled by second order PDEs with use of some initial and boundary
conditions. We use double Laplace transform (DLT) and triple Laplace
transform (TLT) methods to determine these exact analytical solutions.
We provide examples with figures to test effectiveness of this scheme of
Laplace transform
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