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TMF, 2012, Volume 172, Number 1, Pages 64–72 (Mi tmf6940)  

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

Blowup of solutions of a Korteweg–de Vries-type equation

E. V. Yushkov

Lomonosov Moscow State University, Moscow, Russia

Abstract: We investigate the nonlinear third-order differential equation $(u_{xx}-u)_t+u_{xxx}+uu_x=0$ describing the processes in semiconductors with a strong spatial dispersion. We study the problem of the existence of global solutions and obtain sufficient conditions for the absence of global solutions for some initial boundary value problems corresponding to this equation. We consider examples of solution blowup for initial boundary value and Cauchy problems. We use the Mitidieri–Pokhozhaev nonlinear capacity method.

Keywords: initial boundary value problem, solution blowup, global solvability

DOI: https://doi.org/10.4213/tmf6940

Full text: PDF file (384 kB)
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English version:
Theoretical and Mathematical Physics, 2012, 172:1, 932–938

Bibliographic databases:

Document Type: Article
Received: 26.09.2011

Citation: E. V. Yushkov, “Blowup of solutions of a Korteweg–de Vries-type equation”, TMF, 172:1 (2012), 64–72; Theoret. and Math. Phys., 172:1 (2012), 932–938

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6940
  • http://mi.mathnet.ru/eng/tmf/v172/i1/p64

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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. Korpusov M.O. Yushkov E.V., “Local Solvability and Blow-Up For Benjamin-Bona-Mahony-Burgers, Rosenau-Burgers and Korteweg-de Vries-Benjamin-Bona-Mahony Equations”, Electron. J. Differ. Equ., 2014, 69  mathscinet  zmath  isi  elib
    2. M. O. Korpusov, E. V. Yushkov, “Global unsolvability of a nonlinear conductor model in the quasistationary approximation”, Theoret. and Math. Phys., 191:1 (2017), 471–479  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. E. V. Yushkov, M. O. Korpusov, “Gradient blow-up in generalized Burgers and Boussinesq equations”, Izv. Math., 81:6 (2017), 1286–1296  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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