On the properties of solutions of some ultraparabolic equations of the Kolmogorov type on unbounded time intervals

Ivasyshen Stepan Dmytrovych; Ivasyuk Halyna Petrivna; Fratavchan Tonia  Mykhailivna

Ivasyshen Stepan Dmytrovych ¹ , Ivasyuk Halyna Petrivna ² , Fratavchan Tonia Mykhailivna ²

¹ Department of Mathematical Physics and Differential Equations, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, 01001, Ukraine

² Department of Mathematical Modeling, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

Keywords: ultraparabolic equations of the Kolmogorov type

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Abstract

An explicit fundamental solution as well as it’s estimates are constructed for a class of ultraparabolic equations of Kolmogorov type with the constant leading coefficients. The obtained results are used to derive the integral representations of the solutions on unbounded time intervals, to prove the theorem of the zero solution stability, to prove theorems of Liouville type, and to set the correct solvability of the Cauchi problem on the time interval $(0 , ∞)$ and of the problem without initial conditions.

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ACS Style: Ivasyshen, S.D.; Ivasyuk, H.P.; Fratavchan, T.M. On the properties of solutions of some ultraparabolic equations of the Kolmogorov type on unbounded time intervals. Bukovinian Mathematical Journal. 2018, 1
AMA Style: Ivasyshen SD, Ivasyuk HP, Fratavchan TM. On the properties of solutions of some ultraparabolic equations of the Kolmogorov type on unbounded time intervals. Bukovinian Mathematical Journal. 2018; 1(1-2).
Chicago/Turabian Style: Stepan Dmytrovych Ivasyshen, Halyna Petrivna Ivasyuk, Tonia Mykhailivna Fratavchan. 2018. "On the properties of solutions of some ultraparabolic equations of the Kolmogorov type on unbounded time intervals". Bukovinian Mathematical Journal. 1 no. 1-2.

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