Abstract:
The paper discusses the correctness of the inverse problem on finding an unknown coefficient dependent on t in the nonlinear pseudoparabolic equation of the third order with an additional information on the boundary. The existence and uniqueness theorem is proven. The proof of the theorem is carried out by the reduction of the original inverse problem to the equivalent one with an operator equation for the unknown coefficient.
Keywords:
local existence and uniqueness theorem, a priori estimate, inverse problem, nonlinear higher-order equation, pseudoparabolic equation, filtration.
This research was supported by the Government of the Russian Federation, grant 14.Y26.31.0006.
Received: 25.06.2016 Received in revised form: 10.09.2016 Accepted: 20.11.2016
Bibliographic databases:
Document Type:
Article
UDC:517.95
Language: English
Citation:
Anna Sh. Lyubanova, “The inverse problem for the nonlinear pseudoparabolic equation of filtration type”, J. Sib. Fed. Univ. Math. Phys., 10:1 (2017), 4–15
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\paper The inverse problem for the nonlinear pseudoparabolic equation of filtration type
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2017
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\issue 1
\pages 4--15
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\crossref{https://doi.org/10.17516/1997-1397-2017-10-1-4-15}
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Linking options:
https://www.mathnet.ru/eng/jsfu516
https://www.mathnet.ru/eng/jsfu/v10/i1/p4
This publication is cited in the following 3 articles:
S. N. Shergin, E. I. Safonov, S. G. Pyatkov, “On some inverse coefficient problems with the pointwise overdetermination for mathematical models of filtration”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:1 (2019), 82–95
A. Sh. Lyubanova, A. V. Velisevich, “Inverse problems for the stationary and pseudoparabolic equations of diffusion”, Appl. Anal., 98:11 (2019), 1997–2010
S. N. Shergin, “Chislennyi algoritm dlya nekotoroi obratnoi zadachi filtratsii s tochechnym pereopredeleniem”, J. Comp. Eng. Math., 6:3 (2019), 39–53
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