Математика/5. Математическое моделирование

Baimankulov A.

Kostanay State University named after A.Baitursynov, Kazakhstan.

Identification of the diffusion coefficient

Problem is studied in the field of

, (1)

, (2)

(3)

, (4)

where

. (5)

Moisture is given on soil surface to determine the

. (6)

We show that the diffusion coefficient can be determined in an iterative manner.. Let and be two successive approximations coefficient. Corresponding solution of problem (1) - (5) is denoted by and .Then for the difference we obtain the problem:

(7)

. (8)

. (9)

Multiplying (7) by integrating over all points of the domain and assuming that, , we obtain

Performing a transformation on the right side and in view of our assumptions, we have

(10)

Assuming that

,

we obtain the formula from (10)

. (11)

By setting following approximation , determining the condition of monotonicity of the functional

can be expressed by

,

where

Using formula (11) we deduce that

Movement of select by the formula

.

where - sufficiently small number.

function , determined from the solution of the adjoint problem

, (12)

, (13)

References

1.Нерпин С.В., Юзефович Г.И. О расчете нестационарного движения влаги в почве// Доклады ВАСХНИЛ, № 6, 1966.

2.Юзефович Г.И., Янгарбер В.А. Исследование нелинейного уравнения влагопереноса. // Л.: Колос. Сб. трудов по агрофизике, вып. № 14, 1967.

3.Байманкулов А.Т. Определение коэффициента капиллярной диффузии.// Материали за VIII международна научна практична конференция «Бъдещето въпроси от света на науката -2012», т.36, 17-25 декември, 2012, София.