International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: http://www.sciepub.com/journal/ijpdea Editor-in-chief: Mahammad Nurmammadov
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International Journal of Partial Differential Equations and Applications. 2014, 2(1), 1-6
DOI: 10.12691/ijpdea-2-1-1
Open AccessArticle

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

N. Yaremko1, and O. Yaremko1

1Penza State University,str. Lermontov, Penza, Russia

Pub. Date: December 29, 2013

Cite this paper:
N. Yaremko and O. Yaremko. On a New Formulas for a Direct and Inverse Cauchy Problems of Heat Equation. International Journal of Partial Differential Equations and Applications. 2014; 2(1):1-6. doi: 10.12691/ijpdea-2-1-1

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.

Keywords:
heat equation direct/inverse Cauchy problem well-posed/ill-posed problem hermite polynomials poisson integral.

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