Geodesic
On the Solvability of Boundary Value Problems for the Quasilinear Ultraparabolic Equations of Certain Mathematical Models of the Dynamics of Biological Systems
Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 4, pp. 64-78.

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We consider the problem of modeling population dynamics. Mathematically this problem reduces to studying the solvability of a nonlocal boundary value problem for a quasilinear ultraparabolic equation with astronomic time $t$ and biological time $a$ (the age). In the problem under study we prove the existence and uniqueness theorem for regular solutions.
Keywords: population dynamics, nonlinear ultraparabolic equation, nonlocal boundary value problem, properties of solutions.
Mots-clés : existence of solutions 
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A. I. Kozhanov. On the Solvability of Boundary Value Problems for the Quasilinear Ultraparabolic Equations of Certain Mathematical Models of the Dynamics of Biological Systems. Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 4, pp. 64-78. http://geodesic.mathdoc.fr/item/SJIM_2009_12_4_a6/

[1] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vyssh. shkola, M., 1995 | Zbl

[2] Nakhushev A. M., Kemetova R. O., Modelirovanie sotsialno-istoricheskikh i etnicheskikh protsessov, ElFa, Nalchik, 1998

[3] Anikonov Yu. E., “O matematicheskom modelirovanii etnicheskikh protsessov”, Dokl. RAN, 345:1 (1995), 7–9 | Zbl

[4] Ilin O. A., “Ob odnoznachnoi razreshimosti sistemy uravnenii dinamiki vozrastnogo sostava soobschestva biologicheskikh populyatsii”, V Mezhdunar. konf. po matematicheskomu modelirovaniyu, Tez. dokl. (Yakutsk, 24–28 iyulya 2007 g.), Yakutsk, 2007, 87

[5] Beznoschenko N. Ya., “O suschestvovanii resheniya odnoi kraevoi zadachi dlya uravneniya $u_t-Lu=uBu+f$”, Dokl. AN SSSR, 269:6 (1983), 1292–1295 | MR

[6] Beznoschenko N. Ya., “O zadache Koshi dlya uravneniya $u_t-\Delta u+uAu=f$”, Differents. uravneniya, 19:6 (1983), 991–999 | MR

[7] Kozhanov A. I., “Nelineinye nagruzhennye uravneniya i obratnye zadachi”, Zhurn. vychisl. matematiki i mat. fiziki, 44:4 (2004), 694–716

[8] Kozhanov A. I., “Ob odnom nelineinom nagruzhennom parabolicheskom uravnenii i o svyazannoi s nim obratnoi zadache”, Mat. zametki, 76:6. (2004), 840–853 | MR | Zbl

[9] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | Zbl

[10] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[11] Oleinik O. A., Radkevich E. V., “Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Itogi nauki. Ser. Matematika. Matematicheskii analiz. 1969, VINITI, M., 1971, 7–252 | MR | Zbl

[12] Trenogin V. A., Funktsionalnyi analiz, Nauka, M., 1980 | MR | Zbl

[13] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR

[14] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Nauka, M., 1988 | MR