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 Chelyab. Fiz.-Mat. Zh., 2016, Volume 1, Issue 3, Pages 37–62 (Mi chfmj28)

Mathematics

Structure of solutions for model inverse problem for the heat equation in classes of exponential growth functions

I. V. Tikhonova, Yu. V. Gavrisb, T. Z. Adzhievaa

a Lomonosov Moscow State University, Moscow, Russia
b Moscow State Pedagogical University, Moscow, Russia

Abstract: Model inverse problem of finding the inhomogeneous term of the one-dimensional heat equation is considered. The research is performed in classes of exponential growth functions. The condition of uniqueness of solution is established. It is shown that in case of breakdown of this condition any non-trivial solution of exponential growth can be represented as a linear combination of elementary solutions. Examples of special solutions with superexponential growth are given.

Keywords: inverse problem, heat equation, exponential growth functions.

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UDC: 517.95
Revised: 29.09.2016

Citation: I. V. Tikhonov, Yu. V. Gavris, T. Z. Adzhieva, “Structure of solutions for model inverse problem for the heat equation in classes of exponential growth functions”, Chelyab. Fiz.-Mat. Zh., 1:3 (2016), 37–62

Citation in format AMSBIB
\Bibitem{TikGavAdz16} \by I.~V.~Tikhonov, Yu.~V.~Gavris, T.~Z.~Adzhieva \paper Structure of solutions for model inverse problem for the heat equation in classes of exponential growth functions \jour Chelyab. Fiz.-Mat. Zh. \yr 2016 \vol 1 \issue 3 \pages 37--62 \mathnet{http://mi.mathnet.ru/chfmj28}