Protsakh N. P.
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.
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
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.
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.
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.