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

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

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.

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

Scopus:	2-s2.0-85121518757
Elibrary:	48141956
OpenAlex:	W3118812685

DB	Citing
Scopus	14
OpenAlex	8
Elibrary	5