Construction of the fundamental solution of a class of degenerate parabolic equations of high order

  • H.P. Malytska Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • I.V. Burtnyak Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0002-9440-1467
Keywords: degenerated parabolic equations, modified Levy's method, Kolmogorov's equation, fundamental solution, parametrix
Published online: 2020-06-12

Abstract


In the article, using the modified Levy method, a Green's function for a class of ultraparabolic equations of high order with an arbitrary number of parabolic degeneration groups is constructed. The modified Levy method is developed for high-order Kolmogorov equations with coefficients depending on all variables, while the frozen point, which is a parametrix, is chosen so that an exponential estimate of the fundamental solution and its derivatives is conveniently used.

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How to Cite
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Malytska H., Burtnyak I. Construction of the Fundamental Solution of a Class of Degenerate Parabolic Equations of High Order. Carpathian Math. Publ. 2020, 12 (1), 79-87.