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A new mathematical model of heat conduction processes

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Ukrainian Mathematical Journal Aims and scope

Abstract

To describe heat conduction processes and diffusion, a new fourth-order partial differential equation Lu≡α1L1u+α2L2u=0, where L2=L1L1 and L1 is the classical heat conduction operator, which is invariant with respect to the Galielei group, is proposed. We also obtain an integral representation of the solution of the corresponding boundary problem and study solutions of the Cauchy problem of the traveling-wave type, as well as solutions with an exponential and peaking exponential boundary mode.

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Authors and Affiliations

  1. Mathematics Institute, Academy of Sciences of the Ukrainian SSR, Kiev

    V. I. Fushchich, A. S. Galitsyn & A. S. Polubinskii

Authors
  1. V. I. Fushchich
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  2. A. S. Galitsyn
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  3. A. S. Polubinskii
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 237–245, February, 1990.

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Fushchich, V.I., Galitsyn, A.S. & Polubinskii, A.S. A new mathematical model of heat conduction processes. Ukr Math J 42, 210–216 (1990). https://doi.org/10.1007/BF01071016

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  • DOI: https://doi.org/10.1007/BF01071016

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