Abstract
We obtain large time asymptotic expansions of the solution to the Cauchy problem and the first and second boundary value problems for the Sobolev equation in the quadrant.
Similar content being viewed by others
References
Sobolev S. L., “On a new problem of mathematical physics,” Izv. Akad. Nauk SSSR Ser. Mat., 18, No. 1, 3–50 (1954).
Sobolev S. L., “Sur une classe des problemes de physique mathematique,” in: Atti del Simpos. Intern. Appl. Analisi alla Fisica Matematica, 1964, Cagliari-Sassari, Roma, 1965, pp. 192–208.
Zelenyak T. I. and Mikhaĭlov V. P., “The asymptotic behavior as t→∞ of solutions to some boundary value problems of mathematical physics,” in: Partial Differential Equations (Proceedings of the Symposium Dedicated to Academician S. L. Sobolev on His Sixtieth Birthday) [in Russian], Nauka, Moscow, 1970, pp. 96–119.
Gabov S. A. and Sveshnikov A. G., Problems of Dynamics of Stratified Fluids [in Russian], Nauka, Moscow (1986).
Gabov S. A. and Sveshnikov A. G., Linear Problems of the Theory of Nonstationary Internal Waves [in Russian], Nauka, Moscow (1990).
Demidenko G. V. and Uspenskiĭ S. V., Partial Differential Equations and Systems Not Solvable with Respect to the Highest-Order Derivative, Marcel Dekker, New York and Basel (2003).
Sveshnikov A. G., Al’shin A. B., Korpusov M. O., and Pletner Yu. D., Linear and Nonlinear Equations of Sobolev type [in Russian], Fizmatlit, Moscow (2007).
Galpern S. A., “The Cauchy problem for general systems of linear partial differential equations,” Trudy Moskov. Mat. Obshch., 9, 401–423 (1960).
Uspenskiĭ S. V. and Demidenko G. V., “Behavior at infinity of solutions of a problem of S. L. Sobolev,” Siberian Math. J., 24, No. 5, 809–818 (1983).
Maslennikova V. N. and Bogovskij M. E., “On Sobolev systems in the case of two space variables,” Siberian Math. J., 18, No. 5, 770–787 (1978).
Iskenderov B. A., “The behavior of the solution of a mixed problem for the Sobolev equation in a cylindrical domain as t → +∞,” Comput. Math. Math. Phys., 41, No. 9, 1299–1311 (2001).
Iskenderov B. A., Mamedov Dzh. Yu., and Suleĭmanov S. E., “Mixed problem for the equation governing inertia-gravity waves in the Boussinesq approximation in an unbounded cylindrical domain,” Comput. Math. Math. Phys., 49, No. 9, 1583–1600 (2009).
Gel’fand I. M. and Shilov G. E., Generalized Functions. Ed. 2. Spaces of Basic and Generalized Functions [in Russian], Fizmatgiz, Moscow (1958).
Fedoryuk M. V., Asymptotics: Integrals and Series [in Russian], Nauka, Moscow (1978).
Shilov G. E., Mathematical Analysis [in Russian], Fizmatgiz, Moscow (1960).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text Copyright © 2012 Iskenderov B. A. and Mamedov Dzh. Yu.
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 3, pp. 580–596, May–June, 2012.
Rights and permissions
About this article
Cite this article
Iskenderov, B.A., Mamedov, D.Y. Asymptotic expansion at infinity of the solution to the Cauchy problem for the Sobolev equation. Sib Math J 53, 461–476 (2012). https://doi.org/10.1134/S0037446612020279
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446612020279