GEOMETRO-OPTICAL ASYMPTOTIC REPRESENTATIONS OF THE GREENS-FUNCTION ONMOBILE CATACAUSTICS OF SINGULARLY PERTURBED HEAT FIELDS

A method for obtaining asymptotic expansions (AEs) for the Green's fun ction of singularly perturbed boundary value problems of time-dependen t heat conductivity on spatial-temporal catacaustics located in the bo undary layers of mobile boundaries of domains is proposed and justifie d. The method is based on asymptotic analysis of integral representati ons of the Green's functions considered in the form of heat potentials for two types of catacaustics. New types of standard integrals are in troduced for consideration, which are similar in some ways to the Airy and Pierce integrals.