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


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.


Boundary Condition Lateral Surface Space Variable Lebesgue Space Unbounded Domain 
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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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