Mixed problem for a semilinear ultraparabolic equation in an unbounded domain

• Date: 2007
• Main Authors: Lavrenyuk, S. P., Oliskevych, M. O., Лавренюк, С. П., Оліскевич, М. О.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2007
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3420
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We establish conditions for the existence and uniqueness of a solution of the mixed problem for the ultraparabolic equation $$u_t + \sum^m_{i=1}a_i(x, y, t) u_{y_i} - \sum^n_{i,j=1} \left(a_{ij}(x, y, t) u_{x_i}\right)_{x_j} + \sum^n_{i,j=1} b_{i}(x, y, t) u_{x_i} + b_0(x, y, t, u) =$$ $$= f_0(x, y,...