Математика/5. Математическое моделирование

Baimankulov A.

Kostanay State University named after A.Baitursynov, Kazakhstan.

Rating the solution of direct problem

In the area of we consider the problem

, (1)

, (2)

(3)

, (4)

where

. (5)

To determine moisture is given on the soil surface

. (6)

We multiply (1) on and integrate over all internal points of the domain then

Integrating by parts with respect to variable, giving initial and boundary conditions (2) - (4) we obtain

or

+ +

.

After a series of obvious transformations we have

(6)

where

using the inequality

(7)

from (6) we obtain

After application of the Gronwall lemma we obtain the estimate

Based on this evaluation of (7) implies:

Lemma 1. if then for the solution of (1) - (4) we have the estimates:

Consequence. From the obvious equality

implies the estimate

.

Using Lemma 1, we deduce the inequality:

.

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.