Geodesic
Behavior of solutions to an inverse problem for a quasilinear parabolic equation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1393-1409

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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.
Keywords: inverse problems, blowing-up solutions, stability, integral overdetermination condition. 
@article{SEMR_2019_16_a99,
     author = {S. E. Aitzhanov and D. T. Zhanuzakova},
     title = {Behavior of solutions to an inverse problem for a quasilinear parabolic equation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1393--1409},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a99/}
}
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S. E. Aitzhanov; D. T. Zhanuzakova. Behavior of solutions to an inverse problem for a quasilinear parabolic equation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1393-1409. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a99/