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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 6, Pages 65–90 (Mi izv410)  

This article is cited in 5 scientific papers (total in 5 papers)

Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains

G. G. Laptev

Tula State University

Abstract: We establish conditions sufficient for the absence of global solutions of semilinear hyperbolic inequalities and systems in conic domains of the Euclidean space $\mathbb R^N$.
We consider a model problem in a cone $K$: that given by the inequality
$$ \dfrac{\partial^2u}{\partial t^2}-\Delta u\geqslant |u|^q, \qquad (x,t)\in K\times(0,\infty), $$
The proof is based on the test-function method developed by Veron, Mitidieri, Pokhozhaev, and Tesei.

DOI: https://doi.org/10.4213/im410

Full text: PDF file (1590 kB)
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English version:
Izvestiya: Mathematics, 2002, 66:6, 1147–1170

Bibliographic databases:

UDC: 517.9
MSC: 35J60, 35G20, 35B99, 35J65, 35B50
Received: 26.03.2001

Citation: G. G. Laptev, “Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains”, Izv. RAN. Ser. Mat., 66:6 (2002), 65–90; Izv. Math., 66:6 (2002), 1147–1170

Citation in format AMSBIB
\Bibitem{Lap02}
\by G.~G.~Laptev
\paper Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains
\jour Izv. RAN. Ser. Mat.
\yr 2002
\vol 66
\issue 6
\pages 65--90
\mathnet{http://mi.mathnet.ru/izv410}
\crossref{https://doi.org/10.4213/im410}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1970353}
\zmath{https://zbmath.org/?q=an:1078.35140}
\transl
\jour Izv. Math.
\yr 2002
\vol 66
\issue 6
\pages 1147--1170
\crossref{https://doi.org/10.1070/IM2002v066n06ABEH000410}


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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. E. Mitidieri, S. I. Pokhozhaev, “A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities”, Proc. Steklov Inst. Math., 234 (2001), 1–362  mathnet  mathscinet  zmath
    2. Akbar B. Aliev, Anar A. Kazimov, “Existence, non-existence and asymptotic behavior of global solutions to the Cauchy problem for systems of semilinear hyperbolic equations with damping terms”, Nonlinear Analysis: Theory, Methods & Applications, 2011  crossref  mathscinet  isi  scopus
    3. Akbar B. Aliev, Anar A. Kazimov, Vusala F. Guliyeva, “Global existence and nonexistence results for a class of semilinear hyperbolic systems”, Math. Meth. Appl. Sci, 2012, n/a  crossref  mathscinet  isi  scopus
    4. Aliev A.B., Kazimov A.A., “Global Solvability and Behavior of Solutions of the Cauchy Problem for a System of Two Semilinear Hyperbolic Equations with Dissipation”, Differ. Equ., 49:4 (2013), 457–467  crossref  mathscinet  zmath  isi  scopus
    5. Lupo D., Payne K.R., Popivanov N.I., “On the Degenerate Hyperbolic Goursat Problem For Linear and Nonlinear Equations of Tricomi Type”, Nonlinear Anal.-Theory Methods Appl., 108 (2014), 29–56  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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