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Matematicheskie Zametki, 2005, Volume 78, Issue 4, Pages 559–578
DOI: https://doi.org/10.4213/mzm2614
(Mi mzm2614)
 

This article is cited in 3 scientific papers (total in 3 papers)

On the “Destruction” of Solutions of Nonlinear Wave Equations of Sobolev Type with Cubic Sources

M. O. Korpusov, A. G. Sveshnikov

M. V. Lomonosov Moscow State University, Faculty of Physics
Full-text PDF (278 kB) Citations (3)
References:
Abstract: We consider model three-dimensional wave nonlinear equations of Sobolev type with cubic sources, and foremost, model three-dimensional equations of Benjamin–Bona–Mahony and Rosenau types with model cubic sources. An essentially three-dimensional nonlinear equation of spin waves with cubic source is also studied. For these equations, we investigate the first initial boundary-value problem in a bounded domain with smooth boundary. We prove local solvability in the strong generalized sense and, for an equation of Benjamin–Bona–Mahony type with source, we prove the unique solvability of a “weakened” solution. We obtain sufficient conditions for the “destruction” of the solutions of the problems under consideration. These conditions have the sense of a “large” value of the initial perturbation in the norms of certain Banach spaces. Finally, for an equation of Benjamin–Bona–Mahony type, we prove the “failure” of a “weakened” solution in finite time.
Received: 28.10.2003
English version:
Mathematical Notes, 2005, Volume 78, Issue 4, Pages 518–536
DOI: https://doi.org/10.1007/s11006-005-0151-7
Bibliographic databases:
UDC: 519.634
Language: Russian
Citation: M. O. Korpusov, A. G. Sveshnikov, “On the “Destruction” of Solutions of Nonlinear Wave Equations of Sobolev Type with Cubic Sources”, Mat. Zametki, 78:4 (2005), 559–578; Math. Notes, 78:4 (2005), 518–536
Citation in format AMSBIB
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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