A Ray Method for the Asymptotic Solution of the Diffusion Equation

A general method is presented for finding asymptotic solutionsof problems posed for linear partial differential equationscontaining lower order (dispersive) terms. Powers of a largeparameter appear in these equations multiplying the lower orderterms. The expansion procedure is a "ray method", i.e. all ofthe functions that appear in the expansion satisfy ordinarydifferential equations along certain curves called rays. Special attention is paid to the equation of heat conduction.In this case, 1/ is related to the thermal conductivity of themedium. For this equation several problems are considered inwhich the parameter enters the data or the inhomogeneous (source)term in various ways.