Abstract
We prove existence of a strong generalized solution in the Sobolev space W 2 1 to the nonstationary problem for the system of the method of spherical harmonics (MSH) corresponding to the radiation transport problem.
Similar content being viewed by others
References
Marchuk G. I., Numerical Methods for Nuclear Reactor Calculations [in Russian], Atomizdat, Moscow (1958).
Vladimirov V. S., “Mathematical problems of the one–velocity theory of transport of particles,” Trudy Mat. Inst. Akad. Nayk SSSR, 61, 3–158 (1961).
Godunov S. K. and Sultangazin U. M., “On dissipativity of the Vladimirov boundary conditions for a symmetric system of the method of spherical harmonics,” Zh. Vychisl. Mat. i Mat. Fiz., 11, No. 3, 688–704 (1971).
Sultangazin U. M., Methods of Spherical Harmonics and Discrete Ordinates in the Problems of Kinetic Transport Theory [in Russian], Nauka, Alma–Ata (1979).
Smelov V. V., “On symmetrization of the odd P 2N–1–approximation of the one–velocity transport equation,” Zh. Vychisl. Mat. i Mat. Fiz., 20, No. 1, 121–132 (1980).
Smelov V. V., “On the unique determination of the condition on interior and exterior boundaries of the domain in the odd P 2N–1–approximation of the method of spherical harmonics,” Zh. Vychisl. Mat. i Mat. Fiz., 19, No. 1, 248–252 (1979).
Smelov V. V., “The iterated principle over subdomains in the problems with the transport equation,” Zh. Vychisl. Mat. i Mat. Fiz., 21, No. 6, 1493–1504 (1981).
Sultangazin U. M., Smelov V. V., Marek I., Akishev A. Sh., et al., Mathematical Problems of Kinetic Transport Theory [in Russian], Nauka, Alma–Ata (1986).
Weinberg A. M. and Wigner E. P., The Physical Theory of Neutron Chain Reactors [Russian translation], Izdat. Inostr. Lit., Moscow (1961).
Rumyantsev G. Ya., “Boundary Conditions in the Method of Spherical Harmonics,” Atom. Ènerg., 10, No. 1, 26–34 (1961).
Akishev A. Sh., “On one Vladimirov's problem in the radiation transport theory (short report),” Uspekhi Mat. Nauk, 37, No. 5, 227 (1982).
Akishev A. Sh., “On one Vladimirov's problem in the radiation transport theory,” Apl. Mat., 29, No. 3, 161–181 (1984).
Ladyzhenskaya O. A., Boundary Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).
Smelov V. V. and Kutov V. P., Finite P N–Approximations of the Method of Spherical Harmonics with Various Approximations in Different Subdomains [Preprint, No. 502] [in Russian], Novosibirsk (1984).
Murave \(\imath\) L. A., “On asymptotic behavior at large values of time of a solution to one external boundary value problem for the wave equation,” Dokl. Akad. Nauk SSSR, 220, No. 2, 289–292 (1975).
Akishev A. Sh., “Construction of high–precision difference schemes for systems of the method of spherical harmonics,” in: Abstracts: International Symposium “Numerical Methods for Solving a Transport Equation” (26–28 May 1992), Yadernoe Obshch., Moscow, 1992, pp. 16–19.
Lavrent′ev M. A. and Shabat B. V., Methods of the Theory of Functions of Complex Variables [in Russian], Nauka, Moscow (1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Akysh, A.S. On a Strong Solution in the Method of Spherical Harmonics for a Nonstationary Transport Equation. Siberian Mathematical Journal 43, 605–615 (2002). https://doi.org/10.1023/A:1016312000142
Issue Date:
DOI: https://doi.org/10.1023/A:1016312000142