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Mosc. Math. J., 2003, Volume 3, Number 1, Pages 63–84 (Mi mmj76)  

This article is cited in 3 scientific papers (total in 3 papers)

Non-existence of global solutions for higher-order evolution inequalities in unbounded cone-like domains

G. G. Laptev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We use the test function method developed by Mitidieri and Pohozaev to get a priori estimates and non-existence results for semi-linear “higher-order evolution inequalities” in unbounded cone-like domains. As a model we consider the problem in a cone K with the positive initial-boundary conditions
$$ \frac{\partial^ku}{\partial t^k}-\Delta u\ge|u|^q, \quad k=1,2,…; \quad u_{|\partial K\times[0,\infty)}\ge0, \quad \frac{\partial^{k-1}u}{\partial t^{k-1}}|_{t=0}\ge0, $$
where $\Delta$ denotes the Laplace operator.

Key words and phrases: Blow-up, partial differential inequalities, non-existence cone, cone-like domain.

Full text: http://www.ams.org/.../abst3-1-2003.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 35G25; Secondary 35R45, 35K55, 35L70
Received: April 10, 2002
Language: English

Citation: G. G. Laptev, “Non-existence of global solutions for higher-order evolution inequalities in unbounded cone-like domains”, Mosc. Math. J., 3:1 (2003), 63–84

Citation in format AMSBIB
\Bibitem{Lap03}
\by G.~G.~Laptev
\paper Non-existence of global solutions for higher-order evolution inequalities in unbounded cone-like domains
\jour Mosc. Math.~J.
\yr 2003
\vol 3
\issue 1
\pages 63--84
\mathnet{http://mi.mathnet.ru/mmj76}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1996803}
\zmath{https://zbmath.org/?q=an:1057.35101}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Igarashi T., Umeda N., “Existence of Global Solutions in Time for Reaction-Diffusion Systems with Inhomogeneous Terms in Cones”, Hiroshima Math. J., 42:2 (2012), 267–291  mathscinet  zmath  isi
    2. Suzuki R., Umeda N., “Blow-Up of Solutions of a Quasilinear Parabolic Equation”, Proc. R. Soc. Edinb. Sect. A-Math., 142:2 (2012), 425–448  crossref  mathscinet  zmath  isi  elib  scopus
    3. Sun Yu., “The Absence of Global Positive Solutions to Semilinear Parabolic Differential Inequalities in Exterior Domain”, Proc. Amer. Math. Soc., 145:8 (2017), 3455–3464  crossref  zmath  isi  scopus
  • Moscow Mathematical Journal
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