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Matematicheskie Zametki, 2012, Volume 92, Issue 4, Pages 567–582
DOI: https://doi.org/10.4213/mzm9015 (Mi mzm9015) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Blow-Up of the Solution of the Initial Boundary-Value Problem for the Generalized Boussinesq Equation with Nonlinear Boundary Condition

P. A. Makarov

Tikhomirov Instrument Engineering Research Institute
Full-text PDF (485 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm9015
Abstract: The initial boundary-value problem for a nonlinear equation of pseudoparabolic type with nonlinear Neumann boundary condition is considered. We prove a local theorem on the existence of solutions. Using the method of energy inequalities, we obtain sufficient conditions for the blow-up of solutions in a finite time interval and establish upper and lower bounds for the blow-up time.
Keywords: Boussinesq equation, pseudoparabolic-type equation, initial boundary-value problem, Neumann boundary condition, blow-up of solutions, homogenous isotropic semiconductor, Galerkin's method, dissipative processes in a semiconductor.
Received: 07.10.2010
English version:
Mathematical Notes, 2012, Volume 92, Issue 4, Pages 519–531
DOI: https://doi.org/10.1134/S0001434612090246
Bibliographic databases:
Document Type: Article
UDC: 517.958:531.32
Language: Russian
Citation: P. A. Makarov, “Blow-Up of the Solution of the Initial Boundary-Value Problem for the Generalized Boussinesq Equation with Nonlinear Boundary Condition”, Mat. Zametki, 92:4 (2012), 567–582; Math. Notes, 92:4 (2012), 519–531
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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