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Mixed Problem for an Ultraparabolic Equation in Unbounded Domain

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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.

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Authors and Affiliations

  1. Politechnika Krakowska, Kraków, Poland

    S. P. Lavrenyuk

  2. Lviv University, Lviv

    N. P. Protsakh

Authors
  1. S. P. Lavrenyuk
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  2. N. P. Protsakh
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Lavrenyuk, S.P., Protsakh, N.P. Mixed Problem for an Ultraparabolic Equation in Unbounded Domain. Ukrainian Mathematical Journal 54, 1264–1280 (2002). https://doi.org/10.1023/A:1023427422657

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