Geodesic
Analytical solution of the vector model kinetic equations with constant kernel and their applications
Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 2, pp. 283-303 Cet article a éte moissonné depuis la source Math-Net.Ru

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Exact solutions are obtained for the first time for the half-space boundary-value problem for the vector model kinetic equations $$\begin {gathered} \mu \frac {\partial }{\partial x}\Psi (x,\mu )+\Sigma \Psi (x,\mu )=C\int _{-\infty }^{\infty }\exp \left (-{\mu '}^2\right )\Psi (x,\mu ')\,d\mu ',\\ \lim _{x\to 0+}\Psi (x,\mu )=\Psi _0(\mu ),\qquad \mu >0,\\ \lim _{x\to +\infty }\Psi (x,\mu )=A,\qquad \mu <0, \end {gathered} $$ is obtained. Here $x>0$, $\mu \in (-\infty ,0)\cup (0,+\infty )$, $\Sigma =\operatorname {diag}\{\sigma _1,\sigma _2\}$, $C=\left [c_{ij}\right ]$ – $2\times 2$-matrix, $\Psi (x,\mu )$ is vector-column with elements $\psi _1$ and $\psi _2$. As an application, an exact solution is obtained for the first time to the problem of the diffusion slip of a binary gas for a model Boltzmann equation with collision operator in the form proposed by MacCormack. 
@article{TMF_1993_97_2_a9,
     author = {A. V. Latyshev},
     title = {Analytical solution of the vector model kinetic equations with constant kernel and their applications},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {283--303},
     year = {1993},
     volume = {97},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a9/}
}
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A. V. Latyshev. Analytical solution of the vector model kinetic equations with constant kernel and their applications. Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 2, pp. 283-303. http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a9/

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