matmessМатематические заметки СВФУMathematical notes of NEFU2411-93262587-876XСеверо-Восточный федеральный университет имени М.К. Аммосоваmatmess-493Research ArticleМАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕNUMERICALLY SOLVING THE IDENTIFICATION PROBLEM FOR THE LOWER COEFFICIENT OF A PARABOLIC EQUATIONNUMERICALLY SOLVING THE IDENTIFICATION PROBLEM FOR THE LOWER COEFFICIENT OF A PARABOLIC EQUATIONVabishchevichP. N.VabishchevichP. N.

P. N. Vabishchevich

Nuclear Safety Institute, Russian Academy of Sciences 115191, Moscow, Russia 

P. N. Vabishchevich

Nuclear Safety Institute, Russian Academy of Sciences 115191, Moscow, Russia

vabishchevich@gmail.comVasil′evV. I.Vasil′evV. I.

V. I. Vasil′ev

North-Eastern Federal University, 677000, Yakutsk, Russia 

V. I. Vasil′ev

North-Eastern Federal University, 677000, Yakutsk, Russia 

vasvasil@mail.ruNuclear Safety Institute, Russian Academy of SciencesРоссияNuclear Safety Institute, Russian Academy of SciencesRussian FederationNorth-Eastern Federal UniversityРоссияNorth-Eastern Federal UniversityRussian Federation2014100720262147187Copyright © Vabishchevich P.N., Vasil′ev V.I., 20262026Vabishchevich P.N., Vasil′ev V.I.Vabishchevich P.N., Vasil′ev V.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://matmess.elpub.ru/jour/article/view/493

In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the identification problem of coefficients from some additional information. This article deals with the problem of determining in a multidimensional parabolic equation the lower coefficient that depends only on time. To solve numerically a nonlinear inverse problem, linearized approximations in time are constructed using standard finite element procedures in space. The computational algorithm is based on a special decomposition, where the transition to a new time level is implemented via solving two standard elliptic problems. The numerical results presented here for a model 2D problem demonstrate capabilities of the proposed computational algorithms for approximate solving inverse problems.

In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the identification problem of coefficients from some additional information. This article deals with the problem of determining in a multidimensional parabolic equation the lower coefficient that depends only on time. To solve numerically a nonlinear inverse problem, linearized approximations in time are constructed using standard finite element procedures in space. The computational algorithm is based on a special decomposition, where the transition to a new time level is implemented via solving two standard elliptic problems. The numerical results presented here for a model 2D problem demonstrate capabilities of the proposed computational algorithms for approximate solving inverse problems.

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The authors declare that there are no conflicts of interest present.