S. E. Aitzhanov, D. T. Zhanuzakova, “Behavior of solutions to an inverse problem for a quasilinear parabolic equation”, Sib. Èlektron. Mat. Izv., 2019, Volume 16,Pages <nobr>1393

This article is cited in 1 paper

Differentical equations, dynamical systems and optimal control

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

S. E. Aitzhanov^ab, D. T. Zhanuzakova^a

^a Al-Farabi Kazakh National University 71, Al-Farabi ave., Almaty, 050038, Kazakhstan
^b Kazakhstan Institute of Mathematics and Mathematical Modeling 125, Pushkina str., Almaty, 050010, Kazakhstan

Abstract: 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.

Keywords: inverse problems, blowing-up solutions, stability, integral overdetermination condition.

UDC: 517.956

MSC: 35R30,35K55

Received March 20, 2019, published October 9, 2019

Language: English

DOI: 10.33048/semi.2019.16.097