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Ukrainian Mathematical Journal

, Volume 54, Issue 8, pp 1264–1280 | Cite as

Mixed Problem for an Ultraparabolic Equation in Unbounded Domain

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

Abstract

We investigate a mixed problem for a nonlinear ultraparabolic equation in a certain domain Q unbounded in the space variables. This equation degenerates on a part of the lateral surface on which boundary conditions are given. We establish conditions for the existence and uniqueness of a solution of the mixed problem for the ultraparabolic equation; these conditions do not depend on the behavior of the solution at infinity. The problem is investigated in generalized Lebesgue spaces.

Keywords

Boundary Condition Lateral Surface Space Variable Lebesgue Space Unbounded Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • S. P. Lavrenyuk
    • 1
  • N. P. Protsakh
    • 2
  1. 1.Politechnika KrakowskaKrakówPoland
  2. 2.Lviv UniversityLviv

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