ASYMPTOTIC REPRESENTATIONS OF THE SOLUTION TO A SINGULARLY PERTURBED HEAT-CONDUCTIVITY PROBLEM WITH NONLINEAR, EXPONENTIAL-TYPE CONDITIONS ON A MOBILE BOUNDARY

A method for finding approximate values of an irregular, time-dependen t temperature held close to the linear mobile boundary of a bounded do main is proposed and justified. Small values of time, arbitrary temper ature distributions at the initial moment of time, and nonlinear expon ential-type conditions on the mobile boundary are the characteristic f eatures of the problem. The solution is represented as an asymptotic s eries in the sense of Poincare with respect to two small parameters; o ne of them is the boundary-layer variable. Several boundary-layer coef ficients of the asymptotic representation are first calculated explici tly with the help of the specially introduced new standard integral. P roblems important for practical applications are specified, whose appr oximate analytical solutions can be obtained by the method proposed in the paper.