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

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.