- Issue
- Journal of Siberian Federal University. Mathematics & Physics. 2019 12 (4)
- Authors
- Kurilenko, Ilya A.; Shlapunov, Alexander A.
- Contact information
- Kurilenko, Ilya A.: Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia; ; Shlapunov, Alexander A.: Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia;
- Keywords
- the heat equation; ill-posed problems; integral representation method; Carleman formulas
- Abstract
We apply the method of integral representations to study the ill-posed Cauchy problem for the heat equa- tion. 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 H¨older 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
- Pages
- 421–433
- DOI
- 10.17516/1997-1397-2019-12-4-421-433
- Paper at repository of SibFU
- https://elib.sfu-kras.ru/handle/2311/111809
Journal of Siberian Federal University. Mathematics & Physics / On Carleman-type Formulas for Solutions to the Heat Equation
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