On further development of the “method of large λ” in the theory of mixed prOBLEMS: PMM vol. 40, n≗ 3, 1976, pp. 561–565

Abstract

The method of large λ [1], when the solution of the integral equations is represented as an asymptotic expansion in negative powers of some dimensionless parameter λ is used extensively, among the asymptotic methods of investigating the integral equations of the theory of mixed problems. As a rule only several terms of such an asymptotic expansion are constructed successfully. Certain types of integral equations of the second kind, for which a method is proposed for the construction of all terms of the asymptotic expansion, are investigated below by the method of large λ. The coefficients and expansions of the required solution in negative powers of λ are represented as polynomials in the main argument and recursion formulas are obtained for the coefficients of these polynomials. Considered as examples are the axisymmetric mixed nonstationary problem of heat conduction for a homogeneous half-space and the axisymmetric problem of elasticity theory for the torsion of a truncated sphere by a press.