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  4. Properties of fundamental solutions, correct solvability of the Cauchy problem and integral representations of solutions for ultraparabolic Kolmogorov-type equations with three groups of spatial variables and with degeneration on the initial hyperplane

Properties of fundamental solutions, correct solvability of the Cauchy problem and integral representations of solutions for ultraparabolic Kolmogorov-type equations with three groups of spatial variables and with degeneration on the initial hyperplane

MMC.
2022;
Volume 9, Number 3
: pp. 779–790
https://doi.org/10.23939/mmc2022.03.779
Received: April 01, 2022
Revised: September 20, 2022
Accepted: September 21, 2022

Mathematical Modeling and Computing, Vol. 9, No. 3, pp. 779–790 (2022)

Authors:
  1. O. G. Voznyak
  2. V. S. Dron
  3. I. P. Medynskyi
1
West Ukrainian National University
2
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine
3
Lviv Polytechnic National University

Some properties of the fundamental solution of the Cauchy problem for homogeneous ultraparabolic Kolmogorov–type equation with three groups of spatial variables including two groups of degeneration and with degeneration on the initial hyperplane are established. For different type of degeneration on the initial hyperplane the theorems on integral representations of solutions and correct solvability of the Cauchy problem are presented.  These results for such type of equations are obtained in appropriate classes of weight functions.

ultraparabolic equations of the Kolmogorov type
fundamental solution of the Cauchy problem
weight spaces
integral representations of solutions
correct solvability of the Cauchy problem
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