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Matematicheskie Zametki, 2020, Volume 108, Issue 1, Pages 137–152
DOI: https://doi.org/10.4213/mzm12418 (Mi mzm12418) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Solvability of a Mixed Problem with Nonlinear Boundary Condition for a One-Dimensional Semilinear Wave Equation

S. S. Kharibegashvili, O. M. Dzhokhadze

Andrea Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University
Full-text PDF (554 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm12418
Abstract: For a one-dimensional semilinear wave equation, a mixed problem with nonlinear boundary condition is considered. The uniqueness and the local and global solvability of the problem under consideration are studied depending on the type of nonlinearities in the equation and in the boundary conditions. The cases of nonexistence of a solution not only globally but even locally are considered, as well as the case where this problem has a blow-up solution.
Keywords: semilinear wave equation, nonlinear boundary condition, a priori estimate, local and global solvability, nonexistence of a solution, blow-up solutions.
Received: 19.09.2019
English version:
Mathematical Notes, 2020, Volume 108, Issue 1, Pages 123–136
DOI: https://doi.org/10.1134/S0001434620070123
Bibliographic databases:
Document Type: Article
UDC: 517.956.35
Language: Russian
Citation: S. S. Kharibegashvili, O. M. Dzhokhadze, “Solvability of a Mixed Problem with Nonlinear Boundary Condition for a One-Dimensional Semilinear Wave Equation”, Mat. Zametki, 108:1 (2020), 137–152; Math. Notes, 108:1 (2020), 123–136
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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