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Mathematics of the USSR-Sbornik, 1988, Volume 61, Issue 1, Pages 9–22
DOI: https://doi.org/10.1070/SM1988v061n01ABEH003189 (Mi sm1909) 		 
This article is cited in 6 scientific papers (total in 7 papers)

On some nonlinear systems describing the dynamics of competing biological species

A. S. Kalashnikov
English version PDF (657 kB) Citations (7)
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DOI: https://doi.org/10.1070/SM1988v061n01ABEH003189
Abstract: The Cauchy problem is considered for quasilinear degenerate parabolic systems of second order with generally nonsmooth lowest terms. Such systems describe the joint evolution of several biological species consuming the same food. The existence of a generalized solution of this problem is proved, and its behavior for large values of time is studied. In particular, the conditions are found for the survival of individual species and for their extinction in a finite time as well as for boundless proliferation and for spatial localization.
Bibliography: 19 titles.
Received: 21.02.1986
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1987, Volume 133(175), Number 1(5), Pages 11–24
Bibliographic databases:
UDC: 517.956+517.958
MSC: Primary 35K45, 35K55; Secondary 92A15, 35K65
Language: English
Original paper language: Russian
Citation: A. S. Kalashnikov, “On some nonlinear systems describing the dynamics of competing biological species”, Mat. Sb. (N.S.), 133(175):1(5) (1987), 11–24; Math. USSR-Sb., 61:1 (1988), 9–22
Citation in format AMSBIB
\Bibitem{Kal87}
\by A.~S.~Kalashnikov
\paper On some nonlinear systems describing the dynamics of competing biological species
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 133(175)
\issue 1(5)
\pages 11--24
\mathnet{http://mi.mathnet.ru/sm1909}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=898996}
\zmath{https://zbmath.org/?q=an:0657.92010|0642.92015}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 61
\issue 1
\pages 9--22
\crossref{https://doi.org/10.1070/SM1988v061n01ABEH003189}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:338
    Russian version PDF:101
    English version PDF:13
    References:69
     
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