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Ukrainian Mathematical Journal

, Volume 62, Issue 10, pp 1543–1566 | Cite as

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

  • S.D. Ivasyshen
  • V. A. Litovchenko
Article
  • 29 Downloads

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.

Keywords

Positive Constant Cauchy Problem Parabolic Equation Fundamental Solution Vector Genus 
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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • S.D. Ivasyshen
    • 1
  • V. A. Litovchenko
    • 2
  1. 1.“Kyiv Polytechnic Institute”Ukrainian National Technical UniversityKyivUkraine
  2. 2.Fed’kovych Chernivtsi National UniversityChernivtsiUkraine

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