2017
Том 69
№ 6

All Issues

Cauchy problem for a class of degenerate kolmogorov-type parabolic equations with nonpositive genus

Ivasyshen S. D., Litovchenko V. A.

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Abstract

We study the properties of the fundamental solution and establish the correct solvability of the Cauchy problem for a class of degenerate Kolmogorov-type equations with $\{\overrightarrow{p},\overrightarrow{h}\}$-parabolic part with respect to the main group of variables and nonpositive vector genus in the case where the solutions are infinitely differentiable functions and their initial values are generalized functions in the form of Gevrey ultradistributions.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 10, pp 1543-1566.

Citation Example: Ivasyshen S. D., Litovchenko V. A. Cauchy problem for a class of degenerate kolmogorov-type parabolic equations with nonpositive genus // Ukr. Mat. Zh. - 2010. - 62, № 10. - pp. 1330–1350.

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