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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 260, Pages 213–226 (Mi tm596)  
This article is cited in 4 scientific papers (total in 4 papers)

On the Blow-up of Solutions to Nonlinear Initial–Boundary Value Problems

S. I. Pokhozhaev

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (194 kB) Citations (4)
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Abstract: We consider the problem of nonexistence (blow-up) of solutions of nonlinear evolution equations in the case of a bounded (with respect to the space variables) domain. Following the method of nonlinear capacity based on the application of test functions that are optimal (“characteristic”) for the corresponding nonlinear operators, we obtain conditions for the blow-up of solutions to nonlinear initial–boundary value problems. We also show by examples that these conditions are sharp in the class of problems under consideration.
Received in September 2007
English version:
Proceedings of the Steklov Institute of Mathematics, 2008, Volume 260, Pages 204–217
DOI: https://doi.org/10.1134/S008154380801015X
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: S. I. Pokhozhaev, “On the Blow-up of Solutions to Nonlinear Initial–Boundary Value Problems”, Function theory and nonlinear partial differential equations, Collected papers. Dedicated to Stanislav Ivanovich Pohozaev on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 260, MAIK Nauka/Interperiodica, Moscow, 2008, 213–226; Proc. Steklov Inst. Math., 260 (2008), 204–217
Citation in format AMSBIB
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\paper On the Blow-up of Solutions to Nonlinear Initial--Boundary Value Problems
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\pages 213--226
\publ MAIK Nauka/Interperiodica
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Linking options:
  • https://www.mathnet.ru/eng/tm596
  • https://www.mathnet.ru/eng/tm/v260/p213
    • This publication is cited in the following 4 articles:
    1. Matus P.P., Churbanova N.G., Shchadinskii D.A., “On the role of conservation laws and input data in the generation of peaking modes in quasilinear multidimensional parabolic equations with nonlinear source and in their approximations”, Differ. Equ., 52:7 (2016), 942–950  crossref  mathscinet  zmath  isi  elib  scopus
    2. E. V. Yushkov, M. O. Korpusov, “Global Unsolvability of One-Dimensional Problems for Burgers-Type Equations”, Math. Notes, 98:3 (2015), 503–514  mathnet  crossref  crossref  mathscinet  isi  elib
    3. D. A. Schadinskii, “Zakony sokhraneniya i ikh znachenie v razrushenii resheniya v nelineinykh zadachakh dlya parabolicheskikh uravnenii”, Tr. In-ta matem., 23:2 (2015), 103–111  mathnet
    4. P. P. Matus, “Well-posedness of difference schemes for semilinear parabolic equations with weak solutions”, Comput. Math. Math. Phys., 50:12 (2010), 2044–2063  mathnet  crossref  adsnasa
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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    References:130
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