This article is cited in 5 scientific papers (total in 5 papers)
On an ill-posed problem for the heat equation
Roman E. Puzyrev, Alexander A. Shlapunov
Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia
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.
boundary value problems for heat equation, ill-posed problems, integral representation's method.
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Received in revised form: 10.02.2012
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
\by Roman~E.~Puzyrev, Alexander~A.~Shlapunov
\paper On an ill-posed problem for the heat equation
\jour J. Sib. Fed. Univ. Math. Phys.
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