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《Journal of Chongqing Normal University(Natural Science)》 2018-04
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Exact Solutions of One-Dimensional General Heat Conduction Equation

LIN Fubiao;ZHANG Qianhong;ZHANG Jun;LONG Wen;School of Mathematics and Statistics,Guizhou University of Finance and Economics;Guizhou Key Laboratory of Economics System Simulation,Guizhou University of Finance and Economics;  
[Purposes]The exact solutions of one-dimensional general heat conduction equation are constructed.[Methods]Searching for exact solutions of one-dimensional general heat conduction equation is reduced to study and find exact solutions of the corresponding to ordinary differential equation.[Findings]In addition,many new explicit analytical solutions and travelling wave solutions of one-dimensional general heat conduction equation are presented by use of the Lie group analysis method,transformation-trial function method and observational methods.[Conclusions]The new analytical solutions obtained here extend the existing study.
【Fund】: 国家自然科学基金地区科学基金项目(No.11761018;No.11361012;No.61463009);; 贵州省教育厅青年科技人才成长项目(黔教合KY字[2016]170;黔教合KY字[2017]150);; 2017年贵州财经大学校级重点项目(No.2017XZD01)
【CateGory Index】: O175
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