matmessМатематические заметки СВФУMathematical notes of NEFU2411-93262587-876XСеверо-Восточный федеральный университет имени М.К. Аммосова10.25587/SVFU.2021.38.33.008matmess-205Research ArticleМАТЕМАТИКАUNIQUE SOLVABILITY OF CRACK PROBLEM WITH TIME–DEPENDENT FRICTION CONDITION IN LINEARIZED ELASTODYNAMIC BODYUNIQUE SOLVABILITY OF CRACK PROBLEM WITH TIME–DEPENDENT FRICTION CONDITION IN LINEARIZED ELASTODYNAMIC BODYItouH.ItouH.

Hiromichi Itou

Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Hiromichi Itou

Department of Mathematics,

Tokyo University of Science,1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan 

h-itou@rs.tus.ac.jpKashiwabaraT.KashiwabaraT.

Takahito Kashiwabara

Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan 

Takahito Kashiwabara

Graduate School of Mathematical Sciences,

The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan

tkashiwa@ms.u-tokyo.ac.jpDepartment of Mathematics, Tokyo University of ScienceЯпонияDepartment of Mathematics, Tokyo University of ScienceJapanGraduate School of Mathematical Sciences, The University of TokyoЯпонияGraduate School of Mathematical Sciences, The University of TokyoJapan202130032026283121134Copyright © Itou H., Kashiwabara T., 20262026Itou H., Kashiwabara T.Itou H., Kashiwabara T.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/205

This study considers a crack problem with a time-dependent friction condition in a linearized elastodynamic body. We suppose that the crack is fixed and the frictional force acting on the crack is given and depends on the time as well as space variables. The problem is then reduced to a variational inequality of the hyperbolic type. The unique existence of a solution is proved by using Galerkin’s method and deriving a priori estimates for the penalized problem. 

This study considers a crack problem with a time-dependent friction condition in a linearized elastodynamic body. We suppose that the crack is fixed and the frictional force acting on the crack is given and depends on the time as well as space variables. The problem is then reduced to a variational inequality of the hyperbolic type. The unique existence of a solution is proved by using Galerkin’s method and deriving a priori estimates for the penalized problem. 

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