Ukrainian Mathematical Journal

, Volume 58, Issue 9, pp 1347–1368 | Cite as

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

  • S. P. Lavrenyuk
  • N. P. Protsakh
Article

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.

Keywords

Cauchy Problem Diffusion Equation Planck Equation Mixed Problem Kolmogorov Equation 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • S. P. Lavrenyuk
    • 1
  • N. P. Protsakh
    • 2
  1. 1.Lviv National UniversityLviv
  2. 2.Institute for Applied Problems in Mechanics and MathematicsUkrainian Academy of SciencesLviv

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