
On the problem of identification of two lower coefficients and the coefficient by the derivative with respect to time in the parabolic equation
Anzhelika V. Datsenko^{}, Svetlana V. Polyntseva^{} ^{} Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia
Abstract:
The theorem of existence and uniqueness of classical solution of identification problem of two lower coefficients and the coefficient by the derivative with respect to time in the class of smooth bounded functions is proved.
In the proof of the existence and uniqueness of the inverse problem solution using the overdetermination conditions, the original inverse problem is reduced to the direct problem for the loaded (containing traces of unknown functions and their derivatives) equation. The investigation of the correctness of the direct problem is obtained by the method of weak approximation.
Keywords:
identification, inverse problem, parabolic equations, equations in partial derivatives, method of weak approximation.
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UDC:
517.9 Received: 18.05.2011 Received in revised form: 25.09.2011 Accepted: 10.10.2011
Citation:
Anzhelika V. Datsenko, Svetlana V. Polyntseva, “On the problem of identification of two lower coefficients and the coefficient by the derivative with respect to time in the parabolic equation”, J. Sib. Fed. Univ. Math. Phys., 5:1 (2012), 63–74
Citation in format AMSBIB
\Bibitem{DatPol12}
\by Anzhelika~V.~Datsenko, Svetlana~V.~Polyntseva
\paper On the problem of identification of two lower coefficients and the coefficient by the derivative with respect to time in the parabolic equation
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2012
\vol 5
\issue 1
\pages 6374
\mathnet{http://mi.mathnet.ru/jsfu220}
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