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Sbornik: Mathematics, 2014, Volume 205, Issue 4, Pages 573–599
DOI: https://doi.org/10.1070/SM2014v205n04ABEH004388 (Mi sm8249) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Global and blowup solutions of a mixed problem with nonlinear boundary conditions for a one-dimensional semilinear wave equation

S. S. Kharibegashviliab, O. M. Jokhadzeac

a A. Razmadze Mathematical Institute, Georgian Academy of Sciences
b Georgian Technical University
c Tbilisi Ivane Javakhishvili State University
English version PDF (614 kB) Citations (5)
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DOI: https://doi.org/10.1070/SM2014v205n04ABEH004388
Abstract: A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions.
Bibliography: 14 titles.
Keywords: semilinear wave equation, nonlinear boundary conditions, a priori estimate, comparison theorems, global and blowup solutions.
Received: 30.05.2013
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 4, Pages 121–148
DOI: https://doi.org/10.4213/sm8249
Bibliographic databases:
Document Type: Article
UDC: 517.956.35
MSC: Primery 35L20, Secondary 35L70
Language: English
Original paper language: Russian
Citation: S. S. Kharibegashvili, O. M. Jokhadze, “Global and blowup solutions of a mixed problem with nonlinear boundary conditions for a one-dimensional semilinear wave equation”, Mat. Sb., 205:4 (2014), 121–148; Sb. Math., 205:4 (2014), 573–599
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v205/i4/p121
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:64
    First page:34
     
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