Mixed problem for a semilinear ultraparabolic equation in an unbounded domain - Lavrenyuk, S. P.; Oliskevych, M. O. (Ukrains’kyi Matematychnyi Zhurnal, 2007)
We establish conditions for the existence and uniqueness of a solution of the mixed problem for the ultraparabolic equation u_t + ^m_i=1a_i(x, y, t) u_y_i - ^n_i,j=1 (a_ij(x, y, t) u_x_i)_x_j + ^n_i,j=1 b_i(x, y, t) u_x_i + b_0(x, y, t, u) = = f_0(x, y, t, ) - ^n_i=1f_i, x_i (x, y, t) in an unbounded domain with respect to the variables x.