About ellipticity P2 - approximation for the stationary equation of a one - speed transfer

  • S. E. Temirbolat Казахский Национальный Университет имени аль-Фараби
  • G. M. Khushnizarov Казахский Национальный Университет имени аль-Фараби

Abstract

It is considered the P2 - approaching of infinite systems of differential equations, which is obtained by using the spherical harmonics method in stationary kinetic equations of one -speed transfer. In "Mathematical problems of the kinetic theory of transference"the work of U.M. Sultangazin and others it is asserted that stationary equations of one - speed transfer are elliptic, but no proof of the final form of the elliptic system is given. In the non stationary case the system is symmetric hyperbolic by Fredricks, and one can see that becoming process by time, i.e. a process when transient phenomenon becomes stationary, the corresponding operator is elliptic. The above mentioned system is not elliptic after the exclusion of the matrix with time derivatives (form is unknown), the remaining matrices (with derivatives by space variables) are degenerated. Therefore, we will do the following analysis of these systems (P2 - approximation) to establish their ellipticity in line with first - order system of non-degenerated matrices.

References

[1] Султангазин У.М., Смелов В.В., Акишев А.Ш., Сакабеков А., Марек И., Мика С., Житны К. Математические проблемы кинетической теории переноса. – Алма - Ата: Наука, 1986. – 255 с.

[2] Темирболат С. Е. Новая методика исследования некорректных краевых задач. – Алматы: Қазақ университетi, 2009. – 62 с.
How to Cite
TEMIRBOLAT, S. E.; KHUSHNIZAROV, G. M.. About ellipticity P2 - approximation for the stationary equation of a one - speed transfer. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 76, n. 1, p. 53-59, feb. 2015. ISSN 1563-0277. Available at: <http://bm.kaznu.kz/index.php/kaznu/article/view/87>. Date accessed: 23 may 2019.
Section
Mechanics, Mathematics, Computer Science

Keywords

stationary equations of a one - speed transfer; P2 – approximation;