Geodesic
On an ill-posed problem for the heat equation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 3, pp. 337-348

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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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Roman E. Puzyrev; Alexander A. Shlapunov. On an ill-posed problem for the heat equation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 3, pp. 337-348. http://geodesic.mathdoc.fr/item/JSFU_2012_5_3_a4/