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Sbornik: Mathematics, 2008, Volume 199, Issue 9, Pages 1355–1365
DOI: https://doi.org/10.1070/SM2008v199n09ABEH003963 (Mi sm4507) 		 
This article is cited in 15 scientific papers (total in 15 papers)

On blow-up of solutions of the Kuramoto-Sivashinsky equation

S. I. Pokhozhaev

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (285 kB) Citations (15)
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DOI: https://doi.org/10.1070/SM2008v199n09ABEH003963
Abstract: The problem of the absence of global solutions of initial-boundary value problems for the Kuramoto-Sivashinsky equation is considered. Sufficient conditions for the absence of global solutions of the problems under consideration are obtained both for bounded and unbounded domains. These conditions imply a priori the blow-up of the solution of the corresponding initial-boundary value problem. The proof uses a generalization of the method of non-linear capacity based on the choice of asymptotically optimal test functions.
Bibliography: 20 titles.
Received: 16.01.2008
Russian version:
Matematicheskii Sbornik, 2008, Volume 199, Number 9, Pages 97–106
DOI: https://doi.org/10.4213/sm4507
Bibliographic databases:
Document Type: Article
UDC: 517.954
MSC: Primary 35Q53; Secondary 35B05, 35B33, 35B45, 35K55
Language: English
Original paper language: Russian
Citation: S. I. Pokhozhaev, “On blow-up of solutions of the Kuramoto-Sivashinsky equation”, Mat. Sb., 199:9 (2008), 97–106; Sb. Math., 199:9 (2008), 1355–1365
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:76
    First page:37
     
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