Skip to main content
Log in

Cauchy problem for a class of degenerate kolmogorov-type parabolic equations with nonpositive genus

  • Published:
Ukrainian Mathematical Journal Aims and scope

We study the properties of the fundamental solution and establish the correct solvability of the Cauchy problem for a class of degenerate Kolmogorov-type equations with \( \left\{ {\overrightarrow p, \overrightarrow h } \right\} \)-parabolic part with respect to the main group of variables and nonpositive vector genus in the case where the solutions are infinitely differentiable functions and their initial values are generalized functions in the form of Gevrey ultradistributions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. N. Kolmogoroff, “Zufällige Bewegungen (Zur Theorie der Brownschen Bewegung),” Ann. Math., 35, 116–117 (1934).

    Article  MathSciNet  Google Scholar 

  2. S. D. Eidelman, S. D. Ivasyshen, and A. N. Kochubei, Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type (Operator Theory: Advances and Applications), Birkhäuser, Basel (2004).

    Google Scholar 

  3. S. D. Ivasyshen and V. A. Litovchenko, “Cauchy problem for one class of degenerate Kolmogorov-type parabolic equations with positive genus,” Ukr. Mat. Zh., 61, No. 8, 1066–1087 (2009).

    Article  MATH  Google Scholar 

  4. V. A. Litovchenko, “Cauchy problem for \( \left\{ {\overrightarrow p, \overrightarrow h } \right\} \)-parabolic equations with time-dependent coefficients,” Mat. Zametki, 77, No. 3–4, 364–379 (2005).

    MathSciNet  MATH  Google Scholar 

  5. I. M. Gel’fand and G. E. Shilov, Some Problems in the Theory of Differential Equations [in Russian], Fizmatgiz, Moscow (1958).

    Google Scholar 

  6. I. M. Gel’fand and G. E. Shilov, Spaces of Test and Generalized Functions [in Russian], Fizmatgiz, Moscow (1958).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 10, pp. 1330–1350, October, 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ivasyshen, S., Litovchenko, V.A. Cauchy problem for a class of degenerate kolmogorov-type parabolic equations with nonpositive genus. Ukr Math J 62, 1543–1566 (2011). https://doi.org/10.1007/s11253-011-0448-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-011-0448-5

Keywords

Navigation