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Nonlinear differential equations from biology. (English) Zbl 0539.35006
Nonlinear analysis, function spaces and applications, Vol. 2, Proc. Spring Sch., Písek/Czech. 1982, Teubner-Texte Math. 49, 93-125 (1982).
[For the entire collection see Zbl 0488.00011.]
In this paper the author shows that a certain epidemiological model is described by an infinite system of ordinary differential equations. Using a certain procedure, the author reduces this problem to a mixed problem. In the case in which the member of individuals does not depend on time, the mixed problem is reduced to a more simple problem for which the solution is explicitly obtained. Moreover, for this case the behaviour of stationary solutions is studied.
The author has also studied some biological models which are described by Neumann problems for the diffusion equation and a model from population genetics. For the last model he has studied the behaviour of stationary points. Some other interesting models of differential equations are studied both from a theoretical and applicational point of view.
Reviewer: N.Luca
MSC:
35B40 Asymptotic behavior of solutions to PDEs
92D25 Population dynamics (general)
35F30 Boundary value problems for nonlinear first-order PDEs
35J60 Nonlinear elliptic equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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