Inverse Problem for an Equation with A Nonstandard Growth Condition Full article
| Journal |
Journal of Applied Mechanics and Technical Physics
ISSN: 0021-8944 |
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| Output data | Year: 2019, Volume: 60, Number: 2, Pages: 265-277 Pages count : 13 DOI: 10.1134/s0021894419020081 | ||||
| Tags | asymptotic solution behavior; blow-up of the solution; integral overdetermination condition; inverse problem; parabolic equations with a nonstandard growth condition; solvability | ||||
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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 solution for a finite time in a limited region with a homogeneous Dirichlet condition on its boundary are obtained. 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.
Cite:
Antontsev S.N.
, Aitzhanov S.E.
Inverse Problem for an Equation with A Nonstandard Growth Condition
Journal of Applied Mechanics and Technical Physics. 2019. V.60. N2. P.265-277. DOI: 10.1134/s0021894419020081 WOS Scopus РИНЦ OpenAlex
Inverse Problem for an Equation with A Nonstandard Growth Condition
Journal of Applied Mechanics and Technical Physics. 2019. V.60. N2. P.265-277. DOI: 10.1134/s0021894419020081 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000470672500008 |
| Scopus: | 2-s2.0-85066481673 |
| Elibrary: | 38243508 |
| OpenAlex: | W2948256641 |