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Correct Solvability of the Cauchy Problem and Integral Representations of the Solutions for Ultraparabolic Kolmogorov-Type Equations with Two Groups of Spatial Variables of Degeneration

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We establish some properties of the classical fundamental solution of the Cauchy problem for an inhomogeneous ultraparabolic Kolmogorov-type equation with two groups of spatial variables of degeneration, as well as the properties of the volume potential generated by this solution. We also present some theorems on the integral representation of the solutions and correct solvability of the Cauchy problem, obtained in the appropriate classes of weight functions.

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  1. Lviv Polytechnic National University, Lviv, Ukraine

    I. P. Medynsky

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Correspondence to I. P. Medynsky.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 62, No. 4, pp. 39–48, October–December, 2019.

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Medynsky, I.P. Correct Solvability of the Cauchy Problem and Integral Representations of the Solutions for Ultraparabolic Kolmogorov-Type Equations with Two Groups of Spatial Variables of Degeneration. J Math Sci 265, 382–393 (2022). https://doi.org/10.1007/s10958-022-06059-5

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