{"title":"Lagrangian based thermal conduction","authors":"Ferenc Márkus, András Szegleti","doi":"10.1016/S0034-4877(22)00064-7","DOIUrl":null,"url":null,"abstract":"<div><p><span>Based on the Lagrangian description of a dissipative oscillator, the </span>Hamiltonian<span> description and the solution of Fourier heat conduction<span> including the initial and boundary conditions are treated here. It is pointed out that the method can be extended to solve thermal problems. It means that a mathematical tool is elaborated here, that enables us to calculate also the complete solution of thermal propagation involving the Maxwell--Cattaneo--Vernotte (MCV) telegrapher type. In other words, we can solve transport equations described by linear partial differential equations, in general, in which both the initial and the boundary conditions are taken into account. The presented study offers a new kind of numerical solution to certain partial differential equations.</span></span></p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"90 2","pages":"Pages 185-191"},"PeriodicalIF":1.0000,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487722000647","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Based on the Lagrangian description of a dissipative oscillator, the Hamiltonian description and the solution of Fourier heat conduction including the initial and boundary conditions are treated here. It is pointed out that the method can be extended to solve thermal problems. It means that a mathematical tool is elaborated here, that enables us to calculate also the complete solution of thermal propagation involving the Maxwell--Cattaneo--Vernotte (MCV) telegrapher type. In other words, we can solve transport equations described by linear partial differential equations, in general, in which both the initial and the boundary conditions are taken into account. The presented study offers a new kind of numerical solution to certain partial differential equations.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
