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An inverse problem for the pseudo-parabolic equation with p-Laplacian Full article

Journal Evolution Equations and Control Theory
ISSN: 2163-2472
Output data Year: 2022, Volume: 11, Number: 2, Pages: 399-414 Pages count : 16 DOI: 10.3934/eect.2021005
Tags Asymptotic behavior of the solution; Blow-up solution; Inverse problem; Non-local overdetermination condition; Pseudo-parabolic equations; Solvability
Authors Antontsev Stanislav Nikolaevich 1 , Aitzhanov Serik Ersultanovich 2,3 , Ashurova Guzel Rashitkhuzhakyzy 3
Affiliations
1 Lavrentyev Institute of Hydrodynamics of SB RAS, Novosibirsk, Russia
2 Al-Farabi Kazakh National University
3 Institute of Mathematics and Mathematical Modeling

Abstract: In this article, we study the inverse problem of determining the right side of the pseudo-parabolic equation with a p-Laplacian and nonlocal integral overdetermination condition. The existence of solutions in a local and global time to the inverse problem is proved by using the Galerkin method. Sufficient conditions for blow-up (explosion) of the local solutions in a finite time are derived. The asymptotic behavior of solutions to the inverse problem is studied for large values of time. Sufficient conditions are obtained for the solution to disappear (vanish to identical zero) in a finite time. The limits conditions that which ensure the appropriate behavior of solutions are considered.
Cite: Antontsev S.N. , Aitzhanov S.E. , Ashurova G.R.
An inverse problem for the pseudo-parabolic equation with p-Laplacian
Evolution Equations and Control Theory. 2022. V.11. N2. P.399-414. DOI: 10.3934/eect.2021005 Scopus РИНЦ OpenAlex
Identifiers:
Scopus: 2-s2.0-85121518757
Elibrary: 48141956
OpenAlex: W3118812685
Citing:
DB Citing
Scopus 19
OpenAlex 16
Elibrary 8
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