Complete Families of Solutions for Parabolic Equations with Analytic Coefficients.

A complete family of solutions is constructed for the general linear second order parabolic equation in one space variable with entire coefficients defined in a domain with moving boundary and for a class of second order parabolic equations in two space variables with entire coefficients defined in a cylindrical domain. The construction is based on the use of integral operators and results on the analytic continuation of solutions to partial differential equations with analytic coefficients. A numerical example is given which uses a complete family of solutions to approximate the solution to the first initial-boundary value problem for a parabolic equation in one space variable defined in a cylindrical domain.