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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 172, Number 1, Pages 64–72
DOI: https://doi.org/10.4213/tmf6940 (Mi tmf6940) 		 
This article is cited in 4 scientific papers (total in 4 papers)

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

E. V. Yushkov

Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (384 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf6940
Abstract: We investigate the nonlinear third-order differential equation (uxx−u)t+uxxx+uux=0(uxx−u)t+uxxx+uux=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.
Received: 26.09.2011
English version:
Theoretical and Mathematical Physics, 2012, Volume 172, Issue 1, Pages 932–938
DOI: https://doi.org/10.1007/s11232-012-0087-5
Bibliographic databases:
Document Type: Article
Language: Russian
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://www.mathnet.ru/eng/tmf6940
  • https://doi.org/10.4213/tmf6940
  • https://www.mathnet.ru/eng/tmf/v172/i1/p64
    • This publication is cited in the following 4 articles:
    1. 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  crossref  mathscinet  isi
    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  zmath  adsnasa  isi  elib
    4. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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