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Matematicheskie Zametki, 2012, Volume 91, Issue 5, Pages 643–653
DOI: https://doi.org/10.4213/mzm9018 (Mi mzm9018) 		 
This article is cited in 10 scientific papers (total in 10 papers)

On the Initial Boundary-Value Problem for a Nonlinear Sobolev-Type Equation with Variable Coefficient

A. I. Aristov
Full-text PDF (421 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm9018
Abstract: We study the initial boundary-value problem for a nonlinear Sobolev-type equation with variable coefficient. We obtain sufficient conditions for both global and local (in time) solvability. In the case of local (but not global) solvability, we obtain upper and lower bounds for the existence time of the solution in the form of explicit and quadrature formulas.
Keywords: nonlinear Sobolev-type equation, initial boundary-value problem, existence time of a solution, Boussinesq equation, Hölder's inequality, blow-up of a solution.
Received: 29.12.2010
Revised: 29.09.2011
English version:
Mathematical Notes, 2012, Volume 91, Issue 5, Pages 603–612
DOI: https://doi.org/10.1134/S000143461205001X
Bibliographic databases:
Document Type: Article
UDC: 517.955.8
Language: Russian
Citation: A. I. Aristov, “On the Initial Boundary-Value Problem for a Nonlinear Sobolev-Type Equation with Variable Coefficient”, Mat. Zametki, 91:5 (2012), 643–653; Math. Notes, 91:5 (2012), 603–612
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v91/i5/p643
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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