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This article is cited in 6 scientific papers (total in 6 papers)
On Carleman-type formulas for solutions to the heat equation
Ilya A. Kurilenko, Alexander A. Shlapunov Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia
Abstract:
We apply the method of integral representations to study the ill-posed Cauchy problem for the heat equation. More precisely we recover a function, satisfying the heat equation in a cylindrical domain, via its values and 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 (anisotropic) spaces (Sobolev and Hölder spaces, etc). Finally, we obtain a uniqueness theorem for the problem and a criterion of its solvability and a Carleman-type formula for its solution.
Keywords:
the heat equation, ill-posed problems, integral representation method, Carleman formulas.
Received: 28.02.2019 Received in revised form: 11.03.2019 Accepted: 20.04.2019
Citation:
Ilya A. Kurilenko, Alexander A. Shlapunov, “On Carleman-type formulas for solutions to the heat equation”, J. Sib. Fed. Univ. Math. Phys., 12:4 (2019), 421–433
Linking options:
https://www.mathnet.ru/eng/jsfu777 https://www.mathnet.ru/eng/jsfu/v12/i4/p421
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