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Invariant and partially invariant solutions of integro-differential equations for linear thermoviscoelastic aging materials with memory

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Abstract

A linear thermoviscoelastic model for homogeneous, aging materials with memory is established. A system of integro-differential equations is obtained by using two motions (a one-dimensional motion and a shearing motion) for this model. Applying the group analysis method to the system of integro-differential equations, the admitted Lie group is determined. Using this admitted Lie group, invariant and partially invariant solutions are found. The present paper gives a first example of application of partially invariant solutions to integro-differential equations.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550025, Guizhou, China

    Long-Qiao Zhou

  2. School of Mathematics, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand

    Long-Qiao Zhou & Sergey V. Meleshko

Authors
  1. Long-Qiao Zhou
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  2. Sergey V. Meleshko
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Correspondence to Sergey V. Meleshko.

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Communicated by Andreas Öchsner.

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Zhou, LQ., Meleshko, S.V. Invariant and partially invariant solutions of integro-differential equations for linear thermoviscoelastic aging materials with memory. Continuum Mech. Thermodyn. 29, 207–224 (2017). https://doi.org/10.1007/s00161-016-0524-z

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  • DOI: https://doi.org/10.1007/s00161-016-0524-z

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