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Mixed problem for a nonlinear ultraparabolic equation that generalizes the diffusion equation with inertia

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Abstract

We consider a mixed problem for a nonlinear ultraparabolic equation that is a nonlinear generalization of the diffusion equation with inertia and the special cases of which are the Fokker-Planck equation and the Kolmogorov equation. Conditions for the existence and uniqueness of a solution of this problem are established.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1192–1210, September, 2006.

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Lavrenyuk, S.P., Protsakh, N.P. Mixed problem for a nonlinear ultraparabolic equation that generalizes the diffusion equation with inertia. Ukr Math J 58, 1347–1368 (2006). https://doi.org/10.1007/s11253-006-0137-y

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  • DOI: https://doi.org/10.1007/s11253-006-0137-y

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