This article is cited in 1 paper

Mathematics

Problems for McKendrick–von Foerster's equation and their application to the population dynamics of Daphnids: research of toxicity

V. B. Dmitriev^a, Yu. L. Gerasimov<sup>b

a</sup> training center ``Knowledge Plus'', Samara, 443081, Russian Federation
^b Dept. of Zoology, Samara State University, Samara, 443011, Russian Federation

Abstract: In the given work non-local problem with non-linear integral condition for the McKendrick–von Foerster's equation is studied. Estimation of the generalized solution is proved. Also toxicity of grape stones extraction and pomegranate stones extraction is considered by N.S. Stroganov's standart technique and the decision of the McKendrick–von Foerster's equation describing of Daphnids population is showed. The results of the experiments were used for constructing the mortality function, which specify the model for a certain population, and their software simulations were presented. Coefficients of nonlinear multiple regression is computed.

Keywords: nonlocal problem, nonlinear conditions, a priori estimate, generalised solution, grape stones extraction, pomegranate stones extraction, density of Daphnids population.

UDC: 517.956.3+615.453+577.16

Received: 28.10.2010
Revised: 28.10.2010