ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

16. Applications

1991 MS Classification: 34, 35, 92 Yanusi Mahmadyusuf, Tajik State National University, Tajikistan Nonlinear problems with functional initial conditions and its applications The report is devoted to investigations of nonlinear problems with functional initial conditions and determination of its solutions. It is also considered its applications in the field of ecology, economics, hydromechanics and so on. In these problems, the initial condition of Cauchy type is replaced by the initial condition of functional type. For example, the problem of finding the solution of ordinary differential equations

ẋ = f(x, τ), 0 < τ < L with x(0) = ∫_{0}^{L} ϕ(x(ξ), ξ) dξ

is an example of such problems. Here f(·), ϕ(·) are given function, L is given number. In this work we shall investigate nonlinear problems with differential operator of type:

\frac{∂}{∂t} + \frac{∂}{∂a} + ∑_{i} [V_{i} \frac{∂}{∂x_{i}} − \frac{∂}{∂x_{i}} (D_{i} \frac{∂}{∂x_{i}} ) ]

and corresponding initial, functional initial, boundary conditions. Here V_{i} and D_{i} are given matrices, t is time, a is an age, x_{i} are spaces coordinates.

References

1. M. Yunusov, Mathematical models of the struggle with a harmful insects of agrocenos. Dushanbe: Donish, 1991. -143 p.