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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 269, Pages 215–224 (Mi tm2900)  
This article is cited in 4 scientific papers (total in 4 papers)

Blow-up of sign-changing solutions to quasilinear parabolic equations

S. I. Pohozaev

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (172 kB) Citations (4)
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Abstract: We study the blow-up of sign-changing solutions to the Cauchy problem for quasilinear parabolic equations of arbitrary order. Our approach is based on H. Levine's remarkable idea of constructing a concavity inequality for a negative power of a standard positive definite functional. Combining this with the nonlinear capacity method, which is based on the choice of optimal test functions, we find conditions for the blow-up of solutions to the problems under consideration.
Received in September 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 269, Pages 208–217
DOI: https://doi.org/10.1134/S0081543810020185
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: S. I. Pohozaev, “Blow-up of sign-changing solutions to quasilinear parabolic equations”, Function theory and differential equations, Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday, Trudy Mat. Inst. Steklova, 269, MAIK Nauka/Interperiodica, Moscow, 2010, 215–224; Proc. Steklov Inst. Math., 269 (2010), 208–217
Citation in format AMSBIB
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\paper Blow-up of sign-changing solutions to quasilinear parabolic equations
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\bookinfo Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday
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\pages 215--224
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 4 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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