@article{ijpdea2014211,
author={{Yaremko, N. and Yaremko, O.},
title={On a New Formulas for a Direct and Inverse Cauchy Problems of Heat Equation},
journal={International Journal of Partial Differential Equations and Applications},
volume={2},
number={1},
pages={1--6},
year={2014},
url={http://pubs.sciepub.com/ijpdea/2/1/1},
issn={ISSN Pending},
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.},
doi={10.12691/ijpdea-2-1-1}
publisher={Science and Education Publishing}
}