2019
Том 71
№ 1

# Ivasyshen S. D.

Articles: 17
Article (Ukrainian)

### Fundamental solutions of the Cauchy problem for some degenerate parabolic equations of the Kolmogorov type

Ukr. Mat. Zh. - 2011. - 63, № 11. - pp. 1469-1500

Fundamental solutions of the Cauchy problem for three classes of degenerate parabolic equations are investigated. These equations are natural generalizations of the classical Kolmogorov equation of the diffusion with the inertia.

Article (Ukrainian)

### Cauchy problem for a class of degenerate kolmogorov-type parabolic equations with nonpositive genus

Ukr. Mat. Zh. - 2010. - 62, № 10. - pp. 1330–1350

We study the properties of the fundamental solution and establish the correct solvability of the Cauchy problem for a class of degenerate Kolmogorov-type equations with $\{\overrightarrow{p},\overrightarrow{h}\}$-parabolic part with respect to the main group of variables and nonpositive vector genus in the case where the solutions are infinitely differentiable functions and their initial values are generalized functions in the form of Gevrey ultradistributions.

Article (Ukrainian)

### Cauchy problem for one class of degenerate parabolic equations of Kolmogorov type with positive genus

Ukr. Mat. Zh. - 2009. - 61, № 8. - pp. 1066-1087

We investigate properties of a fundamental solution and establish the correct solvability of the Cauchy problem for one class of degenerate Kolmogorov-type equations with $\left\{ {\overrightarrow p, \overrightarrow h } \right\}$-parabolic part with respect to the main group of variables and with positive vector genus in the case where solutions are infinitely differentiable functions and their initial values may be generalized functions of Gevrey ultradistribution type.

Article (Ukrainian)

### Correct solvability of Solonnikov–Eidel’man parabolic initial-value problems

Ukr. Mat. Zh. - 2009. - 61, № 5. - pp. 650-671

We consider initial-value problems for a new class of systems of equations that combine the structures of Solonnikov parabolic systems and Eidel’man parabolic systems. We prove a theorem on the correct solvability of these problems in Hölder spaces of rapidly increasing functions and obtain an estimate for the norms of solutions via the corresponding norms of the right-hand sides of the problem. For the correctness of this estimate, the condition of the parabolicity of the system is not only sufficient but also necessary.

Article (Ukrainian)

### Solonnikov parabolic systems with quasihomogeneous structure

Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1501–1510

We consider a new class of systems of equations that combine the structures of Solonnikov and Éidel’man parabolic systems. We prove a theorem on the reduction of a general initial-value problem to a problem with zero initial data and a theorem on the correct solvability of an initial-value problem in a model case.

Article (Ukrainian)

### On the analyticity of solutions of $\overrightarrow{2b}$-parabolic systems

Ukr. Mat. Zh. - 2006. - 58, № 2. - pp. 160-167

It is proved that if the coefficients of a $\overrightarrow{2b}$ -parabolic system admit analytic extension to a complex region in the space variables, then the fundamental matrix of solutions of the Cauchy problem and regular solutions of the system also possess the same property.

Article (Ukrainian)

### On the Cauchy Problem for $\mathop {2b}\limits^ \to$ -Parabolic Systems with Growing Coefficients

Ukr. Mat. Zh. - 2000. - 52, № 11. - pp. 1484-1496

For $\mathop {2b}\limits^ \to$ -parabolic dissipative systems and systems with growing coefficients as $| x | → ∞$ in the presence of degeneracies in the initial hyperplane, we investigate the fundamental matrix of solutions and the solvability of the Cauchy problem.

Article (Ukrainian)

### Properties of the fundamental solutions and uniqueness theorems for the solutions of the Cauchy problem for one class of ultraparabolic equations

Ukr. Mat. Zh. - 1998. - 50, № 11. - pp. 1482–1496

For one class of degenerate parabolic equations of the Kolmogorov type, we establish the property of normality, the convolution formula, the property of positivity, and a lower bound for the fundamental solution. We also prove uniqueness theorems for the solutions of the Cauchy problem for the classes of functions with bounded growth and for the class of nonnegative functions.

Anniversaries (Russian)

### Samuil Davidovich Eidelman (On his sixtieth birthday)

Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 578

Article (Ukrainian)

### Integral representation and initial values of solutions of 2 b-parabolic systems

Ukr. Mat. Zh. - 1990. - 42, № 4. - pp. 500–506

Article (Ukrainian)

### Asymptotic behavior of solutions of the heat-conduction equation with white noise in the right side

Ukr. Mat. Zh. - 1985. - 37, № 1. - pp. 8 – 20

Article (Ukrainian)

### Parabolic boundary-value problems without initial conditions

Ukr. Mat. Zh. - 1982. - 34, № 5. - pp. 547—552

Article (Ukrainian)

### Correct solvability of parabolic bounbary-value problems in spaces of increasing functions

Ukr. Mat. Zh. - 1982. - 34, № 1. - pp. 20-24

Article (Ukrainian)

### Composition of parabolic kernels

Ukr. Mat. Zh. - 1980. - 32, № 1. - pp. 35 - 45

Article (Ukrainian)

### Correct solvability of general boundary problems for parabolic systems with increasing coefficients

Ukr. Mat. Zh. - 1978. - 30, № 1. - pp. 100–106

Article (Ukrainian)

### Green's matrix for general elliptic boundary-value problems generated by parabolic problems

Ukr. Mat. Zh. - 1977. - 29, № 4. - pp. 519–526

Article (Russian)

### Estimates of Green's function of homogeneous first-boundary problem for a second-order parabolic equation in a noncylindrical region

Ukr. Mat. Zh. - 1969. - 21, № 1. - pp. 15–27

The author is grateful to S. D. Éidel'naan for his interest in the investigation.