This article is cited in 6 papers

On some nonlinear systems describing the dynamics of competing biological species

A. S. Kalashnikov


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.

UDC: 517.956+517.958

MSC: Primary 35K45, 35K55; Secondary 92A15, 35K65

Received: 21.02.1986

 English version: Mathematics of the USSR-Sbornik, 1988, 61:1, 9–22

Bibliographic databases:

• 
•