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Sbornik: Mathematics, 2003, Volume 194, Issue 1, Pages 151–164
DOI: https://doi.org/10.1070/SM2003v194n01ABEH000710 (Mi sm710) 		 
This article is cited in 10 scientific papers (total in 11 papers)

Multidimensional scalar conservation laws

S. I. Pokhozhaev

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (166 kB) Citations (11)
References:
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DOI: https://doi.org/10.1070/SM2003v194n01ABEH000710
Abstract: A new approach, based on a priori estimates, to the demonstration of the occurrence of a gradient catastrophe of solutions of multidimensional scalar conservation laws is considered.
Upper estimates for the time of the gradient catastrophe are derived. A counterexample is presented showing that the estimate so obtained is asymptotically best possible in the general class of problems under consideration.
Received: 07.06.2002
Russian version:
Matematicheskii Sbornik, 2003, Volume 194, Number 1, Pages 147–160
DOI: https://doi.org/10.4213/sm710
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35L65, 35B05
Language: English
Original paper language: Russian
Citation: S. I. Pokhozhaev, “Multidimensional scalar conservation laws”, Mat. Sb., 194:1 (2003), 147–160; Sb. Math., 194:1 (2003), 151–164
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v194/i1/p147
    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:266
    English version PDF:16
    References:52
    First page:3
     
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