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On the fundamental solution of the Cauchy problem for the ultraparabolic Kolmogorov equation with degeneration on the initial hyperplane
Voznyak Olga Grigorivna 1 , Ivasyshen Stepan Dmytrovych 2 , Medynsky Igor 3
1 Department of Economic Cybernetics and Informatics, Ternopil National Economic University, Ternopil, 46009, Ukraine
2 Department of Mathematical Physics and Differential Equations, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, 01001, Ukraine
3 Department of Applied Mathematics, Lviv polytechnic national university, Lviv, 79007, Ukraine
Keywords: the fundamental solution of the Cauchy problem, the ultraparabolic Kolmogorov equation, hyperplane
Abstract
The classical fundamental solution of the Cauchy problem for a ultra-parabolic equation of Kolmogorov type with coefficients depend on part of spatial variables and with degenerations on the initial hyperplane is constructed. Estimates of one's derivatives and their differences are obtained.
References

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Cite
ACS Style
Voznyak, O.G.; Ivasyshen, S.D.; Medynsky, I. On the fundamental solution of the Cauchy problem for the ultraparabolic Kolmogorov equation with degeneration on the initial hyperplane. Bukovinian Mathematical Journal. 2016, 3
AMA Style
Voznyak OG, Ivasyshen SD, Medynsky I. On the fundamental solution of the Cauchy problem for the ultraparabolic Kolmogorov equation with degeneration on the initial hyperplane. Bukovinian Mathematical Journal. 2016; 3(3-4).
Chicago/Turabian Style
Olga Grigorivna Voznyak, Stepan Dmytrovych Ivasyshen, Igor Medynsky. 2016. "On the fundamental solution of the Cauchy problem for the ultraparabolic Kolmogorov equation with degeneration on the initial hyperplane". Bukovinian Mathematical Journal. 3 no. 3-4.
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