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 J. Sib. Fed. Univ. Math. Phys., 2012, Volume 5, Issue 3, Pages 337–348 (Mi jsfu264)

On an ill-posed problem for the heat equation

Roman E. Puzyrev, Alexander A. Shlapunov

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: A boundary value problem for the heat equation is studied. It consists of recovering a function, satisfying the heat equation in a cylindrical domain, via its values ant the values of its normal derivative on a given part of the lateral surface of the cylinder. We prove that the problem is ill-posed in the natural spaces of smooth functions and in the corresponding Hölder spaces; besides, additional initial data do not turn the problem to a well-posed one. Using Integral Representation's Method we obtain Uniqueness Theorem and solvability conditions for the problem.

Keywords: boundary value problems for heat equation, ill-posed problems, integral representation's method.

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UDC: 517.956.4
Accepted: 20.04.2012
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Citation: Roman E. Puzyrev, Alexander A. Shlapunov, “On an ill-posed problem for the heat equation”, J. Sib. Fed. Univ. Math. Phys., 5:3 (2012), 337–348

Citation in format AMSBIB
\Bibitem{PuzShl12} \by Roman~E.~Puzyrev, Alexander~A.~Shlapunov \paper On an ill-posed problem for the heat equation \jour J. Sib. Fed. Univ. Math. Phys. \yr 2012 \vol 5 \issue 3 \pages 337--348 \mathnet{http://mi.mathnet.ru/jsfu264} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
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2. J. Darde, “Iterated quasi-reversibility method applied to elliptic and parabolic data completion problems”, Inverse Probl. Imaging, 10:2 (2016), 379–407
3. K. O. Makhmudov, O. I. Makhmudov, N. N. Tarkhanov, “A Nonstandard Cauchy Problem for the Heat Equation”, Math. Notes, 102:2 (2017), 250–260
4. Ilya A. Kurilenko, Alexander A. Shlapunov, “On Carleman-type formulas for solutions to the heat equation”, Zhurn. SFU. Ser. Matem. i fiz., 12:4 (2019), 421–433
5. I. E. Niezov, “Regulyarizatsiya nestandartnoi zadachi Koshi dlya dinamicheskoi sistemy Lame”, Izv. vuzov. Matem., 2020, no. 4, 54–63
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