Inverse Problem for an Equation with A Nonstandard Growth Condition

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.

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“…We will now consider the problem (8)- (9). If the ratio (10) holds, then the equality (12) follows from it.…”

Section: Equivalent Problemmentioning

confidence: 99%

“…In [9], we investigated the inverse problem of determining the right side for a nonlinear parabolic equation with a non-standard growth condition with an integral overdetermination condition. The existence of local and global time solutions and their uniqueness were proved.…”

mentioning

confidence: 99%

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

Antont︠s︡ev¹,

Aitzhanov²,

Ashurova³

2022

EECT

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“…The conditions are obtained for the destruction of its solution in finite time. The inverse problem of determining the right-hand side of a parabolic equation with a non-standard growth condition is investigated in the work [18]. The existence and uniqueness of a solution to this problem are proved.…”

Section: Introductionmentioning

confidence: 99%

Behavior of solutions to an inverse problem for a quasilinear parabolic equation

Aitzhanov¹,

Zhanuzakova²

2019

Sib. Elektron. Mat. Izv.

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In this article we consider the inverse problem with an integral condition by redefinition for a parabolic type equation. The existence of a weak solution of the inverse problem is proved by the Galerkin method.In a bounded domain with a homogeneous Dirichlet condition, sufficient conditions for the destruction of its solution in a finite time are obtained, and also the stability of the solution for the inverse problem with the opposite sign on the nonlinearity of the power type.

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