Heat flow in a one-dimensional semi-infinite harmonic lattice with an absorbing boundary

Traditionally, absorbing boundary conditions are used to limit the domains of numerical approximation of partial differential equations in infinite domains. In the present paper, the simplest of these conditions is used to obtain an analytical approximation of the solution to the problem of heat propagation in a one-dimensional infinite harmonic lattice consisting of two semi-infinite homogeneous sublattices with different mechanical characteristics.