Solutions of the generalized kinetic model of annihilation for a mixture of particles of two types
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2110-2114
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The evolution of the concentrations of particles of two types that annihilate at collision is considered. The kinetic model describing the dynamics of the mixture is represented by a system of two first-order nonlinear partial differential equations. It is shown that the solutions of this model are related to the solutions of the inhomogeneous transport equations by the Bäcklund transform. Analytic solutions of the problem about penetration of particles of the first type from the left half-plane into the right half-plane occupied by the particles of the second type (the two-dimensional penetration problem or molecular beam problem) and of the problem of outflow of the particles of the first type from a circular source into a domain occupied by the particles of the second type are obtained. Possible generalizations of the model are discussed.
@article{ZVMMF_2016_56_12_a11,
author = {O. V. Ilyin},
title = {Solutions of the generalized kinetic model of annihilation for a mixture of particles of two types},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {2110--2114},
publisher = {mathdoc},
volume = {56},
number = {12},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a11/}
}
TY - JOUR AU - O. V. Ilyin TI - Solutions of the generalized kinetic model of annihilation for a mixture of particles of two types JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2016 SP - 2110 EP - 2114 VL - 56 IS - 12 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a11/ LA - ru ID - ZVMMF_2016_56_12_a11 ER -
%0 Journal Article %A O. V. Ilyin %T Solutions of the generalized kinetic model of annihilation for a mixture of particles of two types %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2016 %P 2110-2114 %V 56 %N 12 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a11/ %G ru %F ZVMMF_2016_56_12_a11
O. V. Ilyin. Solutions of the generalized kinetic model of annihilation for a mixture of particles of two types. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2110-2114. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a11/