Mixed problem for a semilinear ultraparabolic equation in an unbounded domain

  • S. P. Lavrenyuk
  • M. O. Oliskevych


We establish conditions for the existence and uniqueness of a solution of the mixed problem for the ultraparabolic equation $$u_t + \sum^m_{i=1}a_i(x, y, t) u_{y_i} - \sum^n_{i,j=1} \left(a_{ij}(x, y, t) u_{x_i}\right)_{x_j} + \sum^n_{i,j=1} b_{i}(x, y, t) u_{x_i} + b_0(x, y, t, u) =$$ $$= f_0(x, y, t, ) - \sum^n_{i=1}f_{i, x_i} (x, y, t) $$ in an unbounded domain with respect to the variables x.
How to Cite
Lavrenyuk, S. P., and M. O. Oliskevych. “Mixed Problem for a Semilinear Ultraparabolic Equation in an Unbounded Domain”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, no. 12, Dec. 2007, pp. 1661–1673, https://umj.imath.kiev.ua/index.php/umj/article/view/3420.
Research articles