Abstract
This paper is devoted to the proof of the existence of a solution of the Cauchy problem for a system of equations of ultraparabolic type.
Similar content being viewed by others
REFERENCES
S. A. Tersenov, “On the main boundary-value problems for a certain ultraparabolic equation,” Sibirsk. Mat. Zh. [Siberian Math. J.], 40 (1999), no. 6, 1364–1376.
N. S. Genchev, “On ultraparabolic equations,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 151 (1963), no. 2, 205–268.
V. S. Vladimirov and Yu. N. Drozhzhinov, “A generalized Cauchy problem for ultraparabolic equations,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 31 (1967), no. 6, 1341–1360.
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow, 1967.
Sh. Amirov, “A mixed problem for ultraparabolic equations in bounded domains,” in: Well-Posed Boundary-Value Problems for Nonclassical Equations of Mathematical Physics [in Russian] Institute of Mathematics, Siberian Division of the Academy of Sciences of the USSR, Novosibirsk, 1984.
L. G. Gomboev, “On a well-posed problem for an equation of ultraparabolic type,” in: Problems of Differential Equations and Discrete Mathematics [in Russian], Novosibirsk State University, Novosibirsk, 1986, pp. 44–51.
S. G. Pyatkov, “Solvability of boundary-value problems for ultraparabolic equations,” in: Nonclassical Equations and Equations of Mixed Type [in Russian], Institute of Mathematics, Siberian Division of the Academy of Sciences of the USSR, Novosibirsk, 1990, pp. 182–197.
Ya. I. Shatyro, “The first boundary-value problem for a particular ultraparabolic equation,” Differentsial’nye Uravneniya [Differential Equations] (1971), no. 7, 1089–1141.
A. S. Tersenov, “A priori estimates for a class of degenerate parabolic and ultraparabolic equations,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 338 (1994), no. 2, 168–170.
M. Manfredini, “The Dirichlet problem for a class of ultraparabolic equations,” Adv. Differential Equations, 2 (1997), no. 5, 831–866.
S. Polidoro, “On a class of ultraparabolic operators of Kolmogorov-Fokker-Planck type,” Matematiche (Catania), 49 (1994), no. 1, 53–105.
A. M. Il’in, “On a class of ultraparabolic equations,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 159 (1964), no. 6, 1214–1217.
G. Hr. Kirov, “The Dirichlet problem for a certain ultraparabolic equation,” Godisnik Viss. Tehn. Ucebn. Zaved. Mat., 6 (1970), no. 2, 101–118.
Author information
Authors and Affiliations
Additional information
__________
Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 768–774.
Original Russian Text Copyright ©2005 by S. A. Tersenov.
Rights and permissions
About this article
Cite this article
Tersenov, S.A. Cauchy Problem for a System of Equations of Ultraparabolic Type. Math Notes 77, 708–714 (2005). https://doi.org/10.1007/s11006-005-0071-6
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11006-005-0071-6