# Protsakh N. P.

### Inverse Problem for a Semilinear Ultraparabolic Equation with Unknown Right-Hand Side

Ukr. Mat. Zh. - 2014. - 66, № 3. - pp. 333–348

The inverse problem of determination of a time-dependent multiplier of the right-hand side is studied for a semilinear ultraparabolic equation with integral overdetermination condition in a bounded domain. The conditions for the existence and uniqueness of solution of the posed problem are obtained.

### Properties of solutions of a mixed problem for a nonlinear ultraparabolic equation

Ukr. Mat. Zh. - 2009. - 61, № 6. - pp. 795-809

Mixed problems for a nonlinear ultraparabolic equation are considered in domains bounded and unbounded with respect to the space variables. Conditions for the existence and uniqueness of solutions of these problems are established and some estimates for these solutions are obtained.

### Mixed problem for a nonlinear ultraparabolic equation that generalizes the diffusion equation with inertia

Lavrenyuk S. P., Protsakh N. P.

Ukr. Mat. Zh. - 2006. - 58, № 9. - pp. 1192–1210

We consider a mixed problem for a nonlinear ultraparabolic equation that is a nonlinear generalization of the diffusion equation with inertia and the special cases of which are the Fokker-Planck equation and the Kolmogorov equation. Conditions for the existence and uniqueness of a solution of this problem are established.

### Variational Ultraparabolic Inequalities

Lavrenyuk S. P., Protsakh N. P.

Ukr. Mat. Zh. - 2004. - 56, № 12. - pp. 1616-1628

In a bounded domain of the space ℝ^{ n +2}, we consider variational ultraparabolic inequalities with initial condition. We establish conditions for the existence and uniqueness of a solution of this problem. As a special case, we establish the solvability of mixed problems for some classes of nonlinear ultraparabolic equations with nonclassical and classical boundary conditions.

### Mixed Problem for an Ultraparabolic Equation in Unbounded Domain

Lavrenyuk S. P., Protsakh N. P.

Ukr. Mat. Zh. - 2002. - 54, № 8. - pp. 1053-1066

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.