We construct the classical fundamental solution of the Cauchy problem for a degenerate ultraparabolic equation of the Kolmogorov type with two groups of spatial variables of degeneration. Exact estimates of this solution and its derivatives are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. D. Ivasyshen and I. P. Medynsky, “Classical fundamental solutions of the Cauchy problem for ultraparabolic Kolmogorov-type equations with two groups of spatial variables.” in: V. A. Mykhailets’ (editor), Differential Equations and Related Problems of Analysis [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (2016), pp. 108–155.
S. D. Ivasyshen and I. P. Medynsky, “Classical fundamental solution of the Cauchy problem for ultraparabolic Kolmogorov-type equations with two groups of spatial variables of degeneration. I,” Mat. Met. Fiz.-Mekh. Polya,60, No. 3, 9–31 (2017).
S. D. Eidelman, S. D. Ivasyshen, and A. N. Kochubei, Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type, Birkhäuser, Basel (2004), https://doi.org/https://doi.org/10.1007/978-3-0348-7844-9
Author information
Authors and Affiliations
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 60, No. 4, pp. 7–24, October–December, 2017.
Rights and permissions
About this article
Cite this article
Ivasyshen, S.D., Medynsky, I.P. Classical Fundamental Solution of the Cauchy Problem for Ultraparabolic Kolmogorov-Type Equations with Two Groups of Spatial Variables of Degeneration. II. J Math Sci 247, 1–23 (2020). https://doi.org/10.1007/s10958-020-04786-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-020-04786-1