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 Mat. Zametki, 2011, Volume 89, Issue 3, Pages 393–409 (Mi mz9048)

Weighted Identities for the Solutions of Generalized Korteweg–de Vries Equations

S. I. Pokhozhaev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Consider the Korteweg–de Vries equation $u_t+u_{xxx}+uu_{x}=0$ and its generalization $u_t+u_{xxx}+f(u)_{x}=0$. For the solutions of these equations, weighted identities (differential and integral) are obtained. These identities make it possible to establish the blow-up (in finite time) of the solutions of certain boundary-value problems.

Keywords: Korteweg–de Vries equation, initial boundary-value problem, weighted differential inequality, weighted integral inequality, blow-up of solutions, Hölder's inequality, Young's inequality, Dirichlet boundary condition

DOI: https://doi.org/10.4213/mzm9048

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English version:
Mathematical Notes, 2011, 89:3, 382–396

Bibliographic databases:

UDC: 517.954

Citation: S. I. Pokhozhaev, “Weighted Identities for the Solutions of Generalized Korteweg–de Vries Equations”, Mat. Zametki, 89:3 (2011), 393–409; Math. Notes, 89:3 (2011), 382–396

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz9048
• https://doi.org/10.4213/mzm9048
• http://mi.mathnet.ru/eng/mz/v89/i3/p393

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. I. Pohozaev, “On the absence of global solutions of the Korteweg–de Vries equation”, Journal of Mathematical Sciences, 190:1 (2013), 147–156
2. M. O. Korpusov, “Blowup of solutions of nonlinear equations and systems of nonlinear equations in wave theory”, Theoret. and Math. Phys., 174:3 (2013), 307–314
3. M. O. Korpusov, E. V. Yushkov, “Solution blowup for systems of shallow-water equations”, Theoret. and Math. Phys., 177:2 (2013), 1505–1514
4. M. O. Korpusov, E. V. Yushkov, “Local solvability and blow-up for Benjamin-Bona-Mahony-Burgers, Rosenau-Burgers and Korteweg-de Vries-Benjamin-Bona-Mahony equations”, Electron. J. Differential Equations, 2014, 69, 16 pp.
5. Korpusov M. Ovchinnikov A. Sveshnikov A. Yushkov E., “Blow-Up in Nonlinear Equations of Mathematical Physics: Theory and Methods”, Blow-Up in Nonlinear Equations of Mathematical Physics: Theory and Methods, de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter Gmbh, 2018, 1–326
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