Exact linearization of the sliding problem for a dilute gas in the Bhatnagar-Gross-Krook model

On One Nonlinear Boundary-Value Problem in Kinetic Theory of Gases

“…Below, assuming that the initial function G(z) is the local majorant for the function G 0 (z), η is a fixed point for the function G 1 (z), and imposing some natural conditions on the functions G and G 1 , we will prove global solvability of equation (6) in the space of essentially bounded functions.…”

“…Thus, the sequence of measurable functions {U n (x)} ∞ n=0 has a pointwise limit as n → +∞. By B. Levi's theorem, the function U (x) = lim n→∞ U n (x) satisfies equation (6). From (18)- (20), it also follows that…”

“…Boundary-value problem (1)- (4) can be derived from the Boltzmann equation within the framework of one model suggested in [5] and it has important applications in kinetic theory of gases (see [1][2][3][4][5][6] and references therein). By means of equations (1), (4) with boundary value conditions (2), (3), the flow of a gas with average mass velocity U (x) in a half space x > 0 bounded by the plate wall x = 0 is described.…”

“…In the linear case, where G(x) ≡ x, G 1 (x) ≡ x, the investigation of the problem (1)-(4) was carried out in a number of works (see [1,6] and references therein). In all the papers mentioned, the average mass velocity possesses asymptotics O(x) when x tends to +∞.…”

On some nonlinear integral and integro-differential equations with noncompact operators on positive half-line

“…In problem (2)- (3), is a positive scalar parameter of equation (2), and kernels and 1 satisfy the following conditions,…”