1Penza State University,str. Lermontov, Penza, Russia
International Journal of Partial Differential Equations and Applications.
2014,
Vol. 2 No. 1, 1-6
DOI: 10.12691/ijpdea-2-1-1
Copyright © 2013 Science and Education PublishingCite this paper: N. Yaremko, 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.
Correspondence to: N. Yaremko, Penza State University,str. Lermontov, Penza, Russia. Email:
yaremki@mail.ruAbstract
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.
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