Abstract:
This paper describes an inverse problem for determining the right side of a parabolic equation with a nonstandard growth condition and integral overdetermination condition. The Galerkin method is used to prove the existence of two solutions of the inverse problem and their uniqueness, one of them being local and the other one being global in time. Sufficient blow-up conditions for the local condition for a finite time in a limited region with a homogeneous Dirichlet condition on its boundary. The blow-up of the solution is proven using the Kaplan method. The asymptotic behavior of the inverse problem solutions for large time values is investigated. Sufficient conditions for vanishing of the solution for a finite time are obtained. Boundary conditions ensuring the corresponding behavior of the solutions are considered.
Keywords:
inverse problem, integral overdetermination condition, parabolic equations with a nonstandard growth condition, solvability, blow-up of the solution, asymptotic solution behavior.
Citation:
S. N. Antontsev, S. E. Aitzhanov, “Inverse problem for an equation with a nonstandard growth condition”, Prikl. Mekh. Tekh. Fiz., 60:2 (2019), 93–106; J. Appl. Mech. Tech. Phys., 60:2 (2019), 265–277
\Bibitem{AntAit19}
\by S.~N.~Antontsev, S.~E.~Aitzhanov
\paper Inverse problem for an equation with a nonstandard growth condition
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2019
\vol 60
\issue 2
\pages 93--106
\mathnet{http://mi.mathnet.ru/pmtf462}
\crossref{https://doi.org/10.15372/PMTF20190208}
\elib{https://elibrary.ru/item.asp?id=37248712}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2019
\vol 60
\issue 2
\pages 265--277
\crossref{https://doi.org/10.1134/S0021894419020081}
Linking options:
https://www.mathnet.ru/eng/pmtf462
https://www.mathnet.ru/eng/pmtf/v60/i2/p93
This publication is cited in the following 2 articles:
Stanislav Nikolaevich Antontsev, Serik Ersultanovich Aitzhanov, Guzel Rashitkhuzhakyzy Ashurova, “An inverse problem for the pseudo-parabolic equation with p-Laplacian”, EECT, 11:2 (2022), 399
Mohammad Shahrouzi, Jorge Ferreira, Erhan Pişkin, “Stability result for a variable-exponent viscoelastic double-Kirchhoff type inverse source problem with nonlocal degenerate damping term”, Ricerche mat, 2022
Citation in format AMSBIB
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