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Properties of the fundamental solutions and uniqueness theorems for the solutions of the Cauchy problem for one class of ultraparabolic equations

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Abstract

For one class of degenerate parabolic equations of the Kolmogorov type, we establish the property of normality, the convolution formula, the property of positivity, and a lower bound for the fundamental solution. We also prove uniqueness theorems for the solutions of the Cauchy problem for the classes of functions with bounded growth and for the class of nonnegative functions.

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Authors and Affiliations

  1. Chernovtsy University, Chernovtsy

    V. S. Dron’ & S. D. Ivasyshen

Authors
  1. V. S. Dron’
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  2. S. D. Ivasyshen
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1482–1496, November, 1998.

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Dron’, V.S., Ivasyshen, S.D. Properties of the fundamental solutions and uniqueness theorems for the solutions of the Cauchy problem for one class of ultraparabolic equations. Ukr Math J 50, 1692–1709 (1998). https://doi.org/10.1007/BF02524476

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  • DOI: https://doi.org/10.1007/BF02524476

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