2019
Том 71
№ 11

# Malyts’ka H. P.

Articles: 6
Article (Ukrainian)

### On the fundamental solution of the Cauchy problem for Kolmogorov systems of the second order

Ukr. Mat. Zh. - 2018. - 70, № 8. - pp. 1107-1117

We study the structure of the fundamental solution of the Cauchy problem for a class of ultraparabolic equations with finitely many groups of variables degenerating parabolicity.

Article (Ukrainian)

### Systems of equations of Kolmogorov type

Ukr. Mat. Zh. - 2008. - 60, № 12. - pp. 1650–1663

We consider one class of degenerate parabolic systems of equations of the type of diffusion equation with Kolmogorov inertia. For systems whose coefficients may depend only on the time variable, we construct a fundamental matrix of solutions of the Cauchy problem and obtain estimates for this matrix and all its derivatives.

Article (Ukrainian)

### On the maximum principle for ultraparabolic equations

Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 195-201

We prove the maximum principle and various modifications of it for one class of degeneration of parabolic equations.

Article (Russian)

### The third mixed problem for the Sonin equation in a half space

Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1109–1114

We consider follwing mixed boundary-value problem: $$\begin{array}{*{20}c} {u'_t (t,R) + xu'_y (t,R) + yu'_z (t,R) = u''_{x^2 } (t,R) + f(t,R)} \\ {in \Pi _T = \{ (t,R),0< t \leqslant T,R = (x,y,z),R \in E_3 ,0< x\} ,} \\ {u(0,R) = u_0 (R),u'_x (t,0,y,z) + \beta (t)u(t,0,y,z) = g(t,y,z).} \\ \end{array}$$ A solution of this problem is obtained in the form of a potential.

Article (Ukrainian)

### Structure of the fundamental solutions of some ultraparabolic equations of high order

Ukr. Mat. Zh. - 1985. - 37, № 6. - pp. 713–718

Article (Ukrainian)

### First mixed problem in the half space for the Sonin equation

Ukr. Mat. Zh. - 1983. - 35, № 3. - pp. 321 — 326