On a New Formulas for a Direct and Inverse Cauchy Problems of Heat Equation

Abstract

In this paper a solution of the direct Cauchy problems for heat equation is founded in the form of Hermite polynomial series. A well-known classical solution of direct Cauchy problem is represented as Poisson's integral. The author reveals, the formulas obtained by him for solution of the inverse Cauchy problems have a symmetry with respect to the formulas for corresponding direct Cauchy problems. Obtained formulas for solution of the inverse problems can serve as a basis for reg-ularizing computational algorithms while well-known classical formula for the solution of the inverse Cauchy problem can't be a basis for regu-larizing computational algorithms.