Solution to Initial-Boundary Value Problem for the Heat Conductivity Equation With a Discontinuous Coefficient and General Conjugation Conditions
Кoilyshov U. Sadybekov M. Beisenbayeva К.
2025John Wiley and Sons Ltd
International Journal of Mathematics and Mathematical Sciences
2025#2025Issue 1
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. Copyright
classical solution , heat equation , non-self-adjoint problem , Riesz basis , spectral problem
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Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics, Al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of General Engineering, Academy of Logistics and Transport, Almaty, Kazakhstan
Department of Differential Equations
Department of Mathematics
Department of General Engineering
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