Mixed Problem for an Ultraparabolic Equation in Unbounded Domain
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.
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 8, pp 1264-1280.
Citation Example: Lavrenyuk S. P., Protsakh N. P. Mixed Problem for an Ultraparabolic Equation in Unbounded Domain // Ukr. Mat. Zh. - 2002. - 54, № 8. - pp. 1053-1066.