Use of a hyperbolic equation in thermal-conductivity theory

Features of solutions of the classical heat conduction equation are examined, and one solution of the telegraph equation is derived. A paradox of the heat conduction equation involves the apparent instantaneous propagation of the temperature inhomogeneity; this paradox is considered. The telegraph solution which is presented is close to a self-similar solution. The approach leads to a generalization of the Poisson integral for the classical heat conduction equation.