AN INVERSE PROBLEM FOR THE PSEUDO-PARABOLIC EQUATION WITH P-LAPLACIAN

Antontsev S.N. Aitzhanov S.E. Ashurova G.R.
April 2022 American Institute of Mathematical Sciences

Evolution Equations and Control Theory
2022 #11 Issue 2 399 - 414 pp.

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.

Asymptotic behavior of the solution , Blow-up solution , Inverse problem , Non-local overdetermination condition , Pseudo-parabolic equations , Solvability

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Lavrentyev Institute of Hydrodynamics of SB RAS, Novosibirsk, Russian Federation
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Lavrentyev Institute of Hydrodynamics of SB RAS
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling

10 лет помогаем публиковать статьи Международный издатель

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