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Mathematical notes of NEFU, 2021, Volume 28, Issue 3, Pages 121–134
DOI: https://doi.org/10.25587/SVFU.2021.38.33.008 (Mi svfu329) 		 
Mathematics

Unique solvability of crack problem with time-dependent friction condition in linearized elastodynamic body

H. Itoua, T. Kashiwabarab

a Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
b Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan
Full-text PDF (349 kB)
DOI: https://doi.org/10.25587/SVFU.2021.38.33.008
Abstract: 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.
Keywords: crack, friction, linearized elastodynamics.
Funding agency Grant number
Japan Society for the Promotion of Science 18K03380
17H02857
20K14357
Russian Foundation for Basic Research J20-720
H. Itou was partially supported by a Grant-in-Aid for Scientific Research (C) (No. 18K03380) and (B) (No. 17H02857) from the Japan Society for the Promotion of Science (JSPS). T. Kashiwabara was partially supported by a Grant-in-Aid for Early-Career Scientists (No. 20K14357) of JSPS. The authors acknowledge the support from JSPS and RFBR under the Japan-Russia Research Cooperative Program (Project No. J20-720).
Received: 12.05.2021
Accepted: 26.08.2021
Bibliographic databases:
Document Type: Article
UDC: 539.3+517.958
Language: English
Citation: H. Itou, T. Kashiwabara, “Unique solvability of crack problem with time-dependent friction condition in linearized elastodynamic body”, Mathematical notes of NEFU, 28:3 (2021), 121–134
Citation in format AMSBIB
\Bibitem{ItoKas21}
\by H.~Itou, T.~Kashiwabara
\paper Unique solvability of crack problem with time-dependent friction condition in linearized elastodynamic body
\jour Mathematical notes of NEFU
\yr 2021
\vol 28
\issue 3
\pages 121--134
\mathnet{http://mi.mathnet.ru/svfu329}
\crossref{https://doi.org/10.25587/SVFU.2021.38.33.008}
\elib{https://elibrary.ru/item.asp?id=46670180}
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