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Ufimsk. Mat. Zh., 2015, Volume 7, Issue 2, Pages 57–65 (Mi ufa278)  

Täcklind uniqueness classes for heat equation on noncompact Riemannian manifolds

V. F. Vil'danovaa, F. Kh. Mukminovb

a Bashkir State Pedagogical University named after M. Akhmulla, October rev. st., 3a, 450000, Ufa, Russia
b Institute of Mathematics CC USC RAS, Chernyshevskii str., 112, 450008, Ufa, Russia

Abstract: We describe uniqueness classes for solution of the Cauchy problem for the heat equation on a connected noncompact complete Riemannian manifold. For the case of manifolds with boundary, we assume that the solution satisfies the Dirichlet and Neumann conditions on the boundary.
Uniqueness classes are determined by a non-negative function growing no faster than the distance from a fixed point along a geodesics. The classes are similar to uniqueness classes of Täcklind type for the equation on the real line.

Keywords: uniqueness classes, heat equation, Riemannian manifold.

Full text: PDF file (515 kB)
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English version:
Ufa Mathematical Journal, 2015, 7:2, 55–63 (PDF, 349 kB); https://doi.org/10.13108/2015-7-2-55

Bibliographic databases:

UDC: 517.946
MSC: 35K10, 35K20, 35R01, 58J32
Received: 24.11.2014

Citation: V. F. Vil'danova, F. Kh. Mukminov, “Täcklind uniqueness classes for heat equation on noncompact Riemannian manifolds”, Ufimsk. Mat. Zh., 7:2 (2015), 57–65; Ufa Math. J., 7:2 (2015), 55–63

Citation in format AMSBIB
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\pages 57--65
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