Open AccessAn inverse problem for the pseudo-parabolic equation with p-Laplacian
Author(s) -
S. N. Antont︠s︡ev,
Serik Aitzhanov,
Guzel Rashitkhuzhakyzy Ashurova
Publication year - 2022
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2021005
Subject(s) - mathematics , inverse , inverse problem , laplace operator , overdetermination , mathematical analysis , parabolic partial differential equation , partial differential equation , geometry , philosophy , epistemology
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.