2019
Том 71
№ 1

# Oliskevych M. O.

Articles: 2
Article (Ukrainian)

### Mixed problem for a semilinear ultraparabolic equation in an unbounded domain

Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1661–1673

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.

Article (Ukrainian)

### Galerkin Method for First-Order Hyperbolic Systems with Two Independent Variables

Ukr. Mat. Zh. - 2002. - 54, № 10. - pp. 1356-1371

We investigate a mixed problem for a weakly nonlinear first-order hyperbolic system with two independent variables in bounded and unbounded domains. Assuming that the nonlinearities are monotonic, we obtain conditions for the existence and uniqueness of a generalized solution; these conditions do not depend on the behavior of a solution as x → +∞.