Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2016},
     volume = {56},
     number = {12},
     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
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
%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/

[1] Krapivsky P., Redner S., Ben-Naim E., Kinetic view of statistical physics, Cambridge University Press, Cambridge, 2010 | MR | Zbl

[2] ben-Avraham D., Burschka M., Doering C., “Statics and dynamics of a diffusion-limited reaction: anomalous kinetics, noneqnilibrium self-ordering, and a dynamic transition”, J. Stat. Phys., 60 (1990), 695–728 | DOI | MR | Zbl

[3] Marri D., Nelineinye differentsialnye uravneniya v biologii. Lektsii o modelyakh, Mir, M., 1983

[4] Aristov V., Ilin O., “Opisanie bystrykh protsessov vtorzheniya na osnove kineticheskoi modeli”, Komp. issledovaniya i modelirovanie, 6 (2014), 829–838

[5] Aristov V., Ilyin O., “Kinetic models for historical processes of fast invasion and aggression”, Phys. Rev. E, 91 (2015), 042806 | DOI

[6] Weiss J., Tabor M., Carnevale G., “The Painleve property for partial differential equations”, J. Math. Phys., 24 (1983), 522–526 | DOI | MR | Zbl

[7] Weiss J., “On classes of integrable systems and the Painleve property”, J. Math. Phys., 25 (1984), 13–24 | DOI | MR | Zbl

[8] Weiss J., “The Painleve property for partial differential equations. II: Backlund transformation, Lax pairs, and the Schwarzian derivative”, J. Math. Phys., 24 (1983), 1405–1413 | DOI | MR | Zbl

[9] Aristov V., Shakhov E., “Nelineinoe rasseyanie impulsnogo molekulyarnogo puchka v razrezhennom gaze”, Zh. vychisl. matem. i matem. fiz., 27 (1987), 1845–1852

[10] Vladimirov V., Uravneniya matematicheskoi fiziki, Nauka, M., 1981

[11] Sveshnikov A., Bogolyubov A., Kravtsov V., Lektsii po matematicheskoi fizike, Izd-vo MGU, M., 1993