2019
Том 71
№ 8

# Ukrains’kyi Matematychnyi Zhurnal (Ukrainian Mathematical Journal)

Editor-in-Chief: A. M. Samoilenko
ISSN: 0041-6053, 1027-3190

Ukrains'kyi Matematychnyi Zhurnal (UMZh) was founded in May 1949. Journal is issued by Institute of Mathematics NAS of Ukraine. English version is reprinted in the Springer publishing house and called Ukrainian Mathematical Journal.

Ukrains'kyi Matematychnyi Zhurnal focuses on research papers in the principal fields of pure and applied mathematics. The journal is published monthly, each annual volume consists of 12 issues. Articles in Ukrainian, Russian and English are accepted for review.

UMZh indexed in: MathSciNet, zbMATH, Scopus, Web of Science, Google Scholar.

Impact Factor*: 0.189
*2015 Journal Citation Reports, Thomson Reuters

SCImago Journal Rank (SJR) 2015: 0.31; H-index: 13
Source Normalized Impact per Paper (SNIP) 2014: 0.605
Impact per Publication (IPP) 2014: 0.216

Mathematical Citation Quotient (MCQ) 2014: 0.22

## Latest Articles (August 2019)

Brief Communications (English)

### On the Merkulov construction of $A_{ \infty}$ -(co)algebras

Ukr. Mat. Zh. - 2019. - 71, № 8. - pp. 1133-1140

UDC 512.5
The aim of this short note is to complete some aspects of a theorem proved by S. Merkulov in [Int. Math. Res. Not. IMRN. – 1999. – 3. – P. 153 – 167] (Theorem 3.4), as well as to provide a complete proof of the dual result for dg coalgebras.

Article (Russian)

### On the existence, uniqueness, and nonexistence of solutions of one boundary-value problem for a semilinear hyperbolic equation

Ukr. Mat. Zh. - 2019. - 71, № 8. - pp. 1123-1132

UDC 517.956.35
We consider a boundary-value problem for a semilinear hyperbolic equation with iterated multidimensional wave operator in the principal part. The theorems on existence, uniqueness, and nonexistence of solutions of this problem are established.

Article (English)

### Existence of nonnegative solutions for a fractional parabolic equation in the whole space

Ukr. Mat. Zh. - 2019. - 71, № 8. - pp. 1064-1072

UDC 517.9
We study existence of nonnegative solutions for a parabolic problem $\dfrac{\partial u}{\partial t} = - (-\triangle)^{\frac{\alpha}{2}}u + \dfrac{c}{|x|^{\alpha}}u$ in $\mathbb{R}^{d}\times (0, T).$ Here $0<\alpha<\min(2,d),$ $(-\triangle)^{\frac{\alpha}{2}}$ is the fractional Laplacian on $\mathbb{R}^{d}$ and $\mathbb{R}^{d}$ and $u_{0}\in L^{2}(\mathbb{R}^{d}).$