najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2016-7-3-405-409najo-1209Research ArticleMATHEMATICSМАТЕМАТИКАThe problem of kernel determination from viscoelasticity system integro-differential equations for homogeneous anisotropic mediaThe problem of kernel determination from viscoelasticity system integro-differential equations for homogeneous anisotropic mediaDurdievD. K.DurdievD. K.

Bukhara

Bukhara

durdiev65@mail.ruDurdievU. D.DurdievU. D.

Kazan

Kazan

umidjan93@mail.ruBukhara State UniversityУзбекистанBukhara State UniversityUzbekistanKazan Federal UniversityРоссияKazan Federal UniversityRussian Federation20162008202573405409Copyright © Durdiev D.K., Durdiev U.D., 20252025Durdiev D.K., Durdiev U.D.Durdiev D.K., Durdiev U.D.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1209

We consider the problem of reconstructing the time-dependent history of the viscoelasticity medium from the viscoelasticity system of equations for an homogeneous anisotropic medium. As additional information, the Fourier image of the displacement vector for values ν = ν0 6= 0 of transformation parameter is given. It is shown that if the given functions satisfy some conditions of agreement and smoothness, the solution for the posed problem is uniquely defined in the class of a continuous functions and it continuously depends on given functions.

We consider the problem of reconstructing the time-dependent history of the viscoelasticity medium from the viscoelasticity system of equations for an homogeneous anisotropic medium. As additional information, the Fourier image of the displacement vector for values ν = ν0 6= 0 of transformation parameter is given. It is shown that if the given functions satisfy some conditions of agreement and smoothness, the solution for the posed problem is uniquely defined in the class of a continuous functions and it continuously depends on given functions.

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