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Mat. Zametki, 2005, Volume 78, Issue 4, Pages 559–578 (Mi mz2614)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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.

DOI: https://doi.org/10.4213/mzm2614

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English version:
Mathematical Notes, 2005, 78:4, 518–536

Bibliographic databases:

UDC: 519.634
Received: 28.10.2003

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 articles:
    1. Zhou J., “Blow-Up and Exponential Decay of Solutions to a Class of Pseudo-Parabolic Equation”, Bull. Belg. Math. Soc.-Simon Steven, 26:5 (2019), 773–785  crossref  mathscinet  isi
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