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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2017, Volume 58, Issue 4, Pages 22–45
DOI: https://doi.org/10.15372/PMTF20170403 (Mi pmtf678) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Symmetry groups of integrodifferential equations for linear thermoviscoelastic materials with memory

L.-Q. Zhoua, S. V. Meleshkob

a School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou, 550025, China
b School of Mathematics, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand
Full-text PDF (292 kB) Citations (8)
DOI: https://doi.org/10.15372/PMTF20170403
Abstract: The group analysis method is applied to a system of integrodifferential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the governing equations for the system is obtained. Using subalgebras of the admissible Lie algebra, two classes of partially invariant solutions of the considered system of integrodifferential equations are studied.
Keywords: linear thermoviscoelasticity, symmetry groups, partially invariant solutions, integrodifferential equations.
Funding agency Grant number
Guizhou University of Finance and Economics
Received: 30.06.2016
Revised: 28.08.2016
English version:
Journal of Applied Mechanics and Technical Physics, 2017, Volume 58, Issue 4, Pages 587–609
DOI: https://doi.org/10.1134/S0021894417040034
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: L.-Q. Zhou, S. V. Meleshko, “Symmetry groups of integrodifferential equations for linear thermoviscoelastic materials with memory”, Prikl. Mekh. Tekh. Fiz., 58:4 (2017), 22–45; J. Appl. Mech. Tech. Phys., 58:4 (2017), 587–609
Citation in format AMSBIB
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\by L.-Q.~Zhou, S.~V.~Meleshko
\paper Symmetry groups of integrodifferential equations for linear thermoviscoelastic materials with memory
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2017
\vol 58
\issue 4
\pages 22--45
\mathnet{http://mi.mathnet.ru/pmtf678}
\crossref{https://doi.org/10.15372/PMTF20170403}
\elib{https://elibrary.ru/item.asp?id=29823149}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2017
\vol 58
\issue 4
\pages 587--609
\crossref{https://doi.org/10.1134/S0021894417040034}
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    • This publication is cited in the following 8 articles:
    1. Fubiao Lin, Yang Yang, Xinxia Yang, “Exact Solutions of Population Balance Equation with Aggregation, Nucleation, Growth and Breakage Processes, Using Scaling Group Analysis”, Symmetry, 16:1 (2024), 65  crossref
    2. J. R. M. Borhan, Abdul Hamid Ganie, M. Mamun Miah, M. Ashik Iqbal, Aly R. Seadawy, Nidhish Kumar Mishra, “A highly effective analytical approach to innovate the novel closed form soliton solutions of the Kadomtsev–Petviashivili equations with applications”, Opt Quant Electron, 56:6 (2024)  crossref
    3. Fubiao Lin, Yang Yang, Xinxia Yang, Qianhong Zhang, “Preliminary group classification and exact solutions of Smoluchowski equation with a source”, Journal of Computational and Applied Mathematics, 444 (2024), 115770  crossref
    4. Cemil Tunç, Osman Tunç, Jen-Chih Yao, “On the Enhanced New Qualitative Results of Nonlinear Integro-Differential Equations”, Symmetry, 15:1 (2022), 109  crossref
    5. Sedigheh Sabermahani, Yadollah Ordokhani, Parisa Rahimkhani, Studies in Systems, Decision and Control, 340, Topics in Integral and Integro-Differential Equations, 2021, 169  crossref
    6. Fubiao Lin, Qianhong Zhang, “Symmetries and exact solutions of the population balance equation with growth and breakage processes, using group analysis”, Math Methods in App Sciences, 44:5 (2021), 3913  crossref
    7. Fubiao Lin, Qianhong Zhang, “Exact solutions of population balance equations for breakage and growth processes, using group analysis”, Applied Mathematics and Computation, 368 (2020), 124790  crossref
    8. Sergey V. Meleshko, Springer Proceedings in Mathematics & Statistics, 266, Symmetries, Differential Equations and Applications, 2018, 105  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
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