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Solution to Initial-Boundary Value Problem for the Heat Conductivity Equation With a Discontinuous Coefficient and General Conjugation Conditions

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  • Umbetkul Кoilyshov
  • Makhmud Sadybekov
  • Кulnyar Beisenbayeva

Abstract

A solution to the initial-boundary value problem for the heat equation with a discontinuous coefficient and a general conjugation condition is verified using the Fourier method. The problem considered in the paper models the process of heat propagation of a temperature field in a thin rod of finite length, consisting of two sections with different thermal-physical characteristics. In this case, not only the boundary conditions of the first kind are taken into account, but also general conditions at the point of contact of the two media. The existence and uniqueness of a classical solution to the studied problem are proved.

Suggested Citation

  • Umbetkul Кoilyshov & Makhmud Sadybekov & Кulnyar Beisenbayeva, 2025. "Solution to Initial-Boundary Value Problem for the Heat Conductivity Equation With a Discontinuous Coefficient and General Conjugation Conditions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2025, pages 1-9, April.
    • Handle: RePEc:hin:jijmms:2756189
    DOI: 10.1155/ijmm/2756189
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