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Matematicheskie Zametki, 2009, Volume 86, Issue 3, Pages 337–349
DOI: https://doi.org/10.4213/mzm8498 (Mi mzm8498) 		 
This article is cited in 9 scientific papers (total in 9 papers)

On the Absence of Local Solutions of Several Evolutionary Problems

E. I. Galakhov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (530 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm8498
Abstract: We consider the existence problem for local (with respect to time) solutions of quasilinear evolutionary partial differential equations and inequalities with singular coefficients and initial conditions. We obtain sufficient conditions for instantaneous blow-up of solutions and show that the results thus obtained cannot be improved in the function class under study.
Keywords: existence problem, quasilinear evolutionary PDE, weak solution, Dirichlet boundary condition, heat equation, Sobolev space, Carathéodory function.
Received: 27.10.2008
English version:
Mathematical Notes, 2009, Volume 86, Issue 3, Pages 314–324
DOI: https://doi.org/10.1134/S000143460909003X
Bibliographic databases:
UDC: 517.954
Language: Russian
Citation: E. I. Galakhov, “On the Absence of Local Solutions of Several Evolutionary Problems”, Mat. Zametki, 86:3 (2009), 337–349; Math. Notes, 86:3 (2009), 314–324
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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