About one system of integral equations in kinetic theory. (Russian, English) Zbl 1199.45012

Terdzhyan, Ts. E.; Khachatryan, A. Kh.

Zh. Vychisl. Mat. Mat. Fiz. 49, No. 4, 715-721 (2009); translation in Comput. Math., Math. Phys. 49, No. 4, 691-697 (2009).

Summary: One system of convolution integral equations is considered on a half-line with an noninvertible matrix integral operator whose symbol has a fourth-order zero. The application of a special factorization method makes it possible to distinguish noninvertible factors in the original noninvertible operator and reduce the system to a new system with a nonsingular integral operator. A structure theorem on the existence of a solution to the original system is proved.

MSC:

45F15	Systems of singular linear integral equations
45E10	Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
82C40	Kinetic theory of gases in time-dependent statistical mechanics

Keywords:

noninvertible operator; matrix integral operator; factorization; Wiener-Hopf system; system of convolution integral equations