Geodesic
Asymptotics of the solution of a mixed problem for a system of differential equations connected with a positive integral operator
Sbornik. Mathematics, Tome 65 (1990) no. 1, pp. 67-79 
E. I. Volkova. Asymptotics of the solution of a mixed problem for a system of differential equations connected with a positive integral operator. Sbornik. Mathematics, Tome 65 (1990) no. 1, pp. 67-79. http://geodesic.mathdoc.fr/item/SM_1990_65_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A mixed problem is considered for a hyperbolic system of partial differential equations for whose solutions there exist integral representations having a probability-theoretical meaning. It is assumed that the right-hand sides of the system satisfy exponential estimates. Under natural restrictions on the coefficients, the asymptotics of the solutions as $t\to\infty$ are obtained with the help of the theory of linear integral operators with nonnegative kernels, and the theory of branching processes with several types of particles in motion along an interval. Bibliography: 10 titles.

[1] Volkova E. I., “Asimptoticheskoe povedenie pri bolshikh znacheniyakh vremeni resheniya smeshannoi zadachi dlya odnogo klassa sistem differentsialnykh uravnenii v chastnykh proizvodnykh giperbolicheskogo tipa”, UMN, 39:4 (1984), 118

[2] Godunov S. K., Uravneniya matematicheskoi fiziki, Nauka, M., 1979 | MR | Zbl

[3] Petrovskii I. G., Lektsii po teorii obyknovennykh differentsialnykh uravnenii, Izd-vo MGU, M., 1984

[4] Sevastyanov B. A., Vetvyaschiesya protsessy, Nauka, M., 1971 | MR

[5] Volkova E. I., “Nekotorye asimptoticheskie svoistva vetvyaschikhsya protsessov s dvizheniem chastits”, DAN SSSR, 279:2 (1984), 290–293 | MR | Zbl

[6] Volkova E. I., Vetvyaschiesya protsessy s bluzhdaniem chastits po otrezku, Diss. $\dots$ kand. fiz.-matem. nauk, MGU, M., 1985

[7] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969 | MR

[8] Krasnoselskii M. A., Polozhitelnye resheniya operatornykh uravnenii, Fizmatgiz, M., 1962 | MR

[9] Zabreiko P. P., Koshelev A. I., Krasnoselskii M. A. i dr., Integralnye upravneniya, Nauka, M., 1968

[10] Maister P. I., “Vetvyaschiesya diffuzionnye protsessy v neogranichennoi oblasti”, Matem. sb., 114(156) (1981), 406–424 | MR | Zbl