Properties of the fundamental solutions and uniqueness theorems for the solutions of the Cauchy problem for one class of ultraparabolic equations
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 class...
Saved in:
| Date: | 1998 |
|---|---|
| Main Authors: | Ivasyshen, S. D., Drotn', V. S., Івасишен, С. Д., Дронь, В. С. |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1998
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4800 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: | |
Institution
Ukrains’kyi Matematychnyi ZhurnalSimilar Items
Classical fundamental solutions of the Cauchy problem for ultraparabolic Kolmogorov type equations with two groups of spatial variables
by: S. D. Ivasyshen, et al.
Published: (2016)
by: S. D. Ivasyshen, et al.
Published: (2016)
On classical fundamental solutions of the Cauchy problem for ultraparabolic equations of Kolmogorov type with two groups of spatial variables
by: S. D. Ivasyshen, et al.
Published: (2016)
by: S. D. Ivasyshen, et al.
Published: (2016)
Properties of fundamental solutions, theorems on integral representations of solutions and correct solvability of the Cauchy problem for ultraparabolic Kolmogorov-type equations with two groups of spatial variables of degeneration
by: S. D. Ivasyshen, et al.
Published: (2018)
by: S. D. Ivasyshen, et al.
Published: (2018)
Classical fundamental solution of the Cauchy problem for ultraparabolic Kolmogorov-type equations with two groups of spatial variables of degeneration. I
by: S. D. Ivasyshen, et al.
Published: (2017)
by: S. D. Ivasyshen, et al.
Published: (2017)
Classical fundamental solution of the Cauchy problem for ultraparabolic Kolmogorov-type equations with two groups of spatial variables of degeneration. II
by: S. D. Ivasyshen, et al.
Published: (2017)
by: S. D. Ivasyshen, et al.
Published: (2017)
Fundamental solution of the Cauchy problem for one parabolic equation with increasing lowest coefficients
by: S. D. Ivasyshen, et al.
Published: (2014)
by: S. D. Ivasyshen, et al.
Published: (2014)
Fundamental solutions of the Cauchy problem for some degenerate parabolic equations of the Kolmogorov type
by: Ivasyshen, S. D., et al.
Published: (2011)
by: Ivasyshen, S. D., et al.
Published: (2011)
The fundamental solution of the Cauchy problem for degenerated parabolic Kolmogorov type equations of arbitrary order
by: S. D. Ivasyshen, et al.
Published: (2019)
by: S. D. Ivasyshen, et al.
Published: (2019)
Cauchy problem for one class of degenerate parabolic equations of Kolmogorov type with positive genus
by: Ivasyshen, S. D., et al.
Published: (2009)
by: Ivasyshen, S. D., et al.
Published: (2009)
Properties of fundamental solutions, correct solvability of the Cauchy problem and integral representations of solutions for ultraparabolic Kolmogorov–type equations with three groups of spatial variables and with degeneration on the initial hyperplane
by: O. Voznyak, et al.
Published: (2022)
by: O. Voznyak, et al.
Published: (2022)
Kolmogorov’s equation for the Cauchy problem’s solution of one class of linear evolutional equations
by: Mestechkina, T. M., et al.
Published: (1987)
by: Mestechkina, T. M., et al.
Published: (1987)
Fundamental solution of the Cauchy problem for a class of degenerate parabolic pseudo-differential equations
by: V. A. Litovchenko
Published: (2013)
by: V. A. Litovchenko
Published: (2013)
Complete analytical description of the fundamental solution of the one parabolic equation with increasing coefficients
by: T. O. Zabolotko, et al.
Published: (2014)
by: T. O. Zabolotko, et al.
Published: (2014)
On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations
by: Kulinich, G. L., et al.
Published: (2004)
by: Kulinich, G. L., et al.
Published: (2004)
One method for the investigation of the fundamental solution of the Cauchy problem for parabolic systems
by: V. A. Litovchenko
Published: (2018)
by: V. A. Litovchenko
Published: (2018)
One method for the investigation of the fundamental solution of the Cauchy
problem for parabolic systems
by: Litovchenko, V. A., et al.
Published: (2018)
by: Litovchenko, V. A., et al.
Published: (2018)
On uniqueness of the Cauchy problem solution for some systems of equations with variable coefficients
by: Chaus, N. N., et al.
Published: (1970)
by: Chaus, N. N., et al.
Published: (1970)
General Theorems on the Existence and Uniqueness of Solutions of Impulsive Differential Equations
by: Slyusarchuk, V. E., et al.
Published: (2000)
by: Slyusarchuk, V. E., et al.
Published: (2000)
In bifurcated solution of the Cauchy problem for one class of parabolic systems
by: Lenуuk, M. P., et al.
Published: (1970)
by: Lenуuk, M. P., et al.
Published: (1970)
Existence and uniqueness of solution of the Cauchy problem for singular systems of integro-differential equations
by: Shmarda, Z., et al.
Published: (1993)
by: Shmarda, Z., et al.
Published: (1993)
One class of multidimensional stochastic differential equations having no property of weak uniqueness of a solution
by: Aryasova, O.V., et al.
Published: (2005)
by: Aryasova, O.V., et al.
Published: (2005)
Principle of localization of solutions of the Cauchy problem for one class of degenerate parabolic equations of Kolmogorov type
by: Litovchenko, V. A., et al.
Published: (2010)
by: Litovchenko, V. A., et al.
Published: (2010)
Correct solvability of the Cauchy problem and integral representations of solutions for ultraparabolic Kolmogorov-type equations with two groups of spatial variables of degeneration
by: I. P. Medynskyi
Published: (2019)
by: I. P. Medynskyi
Published: (2019)
On Periodic Solutions of One Class of Systems of Differential Equations
by: Korol', I. I., et al.
Published: (2005)
by: Korol', I. I., et al.
Published: (2005)
Cauchy problem for a class of degenerate kolmogorov-type parabolic equations with nonpositive genus
by: Ivasyshen, S. D., et al.
Published: (2010)
by: Ivasyshen, S. D., et al.
Published: (2010)
One method for solution of the Cauchy problem for singular parabolic equations
by: Matiichuk , M. I., et al.
Published: (1992)
by: Matiichuk , M. I., et al.
Published: (1992)
Properties of solutions of a mixed problem for a nonlinear ultraparabolic equation
by: Protsakh, N. P., et al.
Published: (2009)
by: Protsakh, N. P., et al.
Published: (2009)
On asymptotics of solutions of one Cauchy’s problem
by: Zernov , A. E., et al.
Published: (2025)
by: Zernov , A. E., et al.
Published: (2025)
On partial solutions of one equation with multiple characteristics and some properties of the fundamental solution
by: Ju. Irgashev
Published: (2016)
by: Ju. Irgashev
Published: (2016)
On partial solutions of one equation with multiple characteristics and some properties of the fundamental solution
by: Irgashev, B. Yu., et al.
Published: (2016)
by: Irgashev, B. Yu., et al.
Published: (2016)
Existence and uniqueness of solution to the Cauchy problem for neutral stochastic differential equation of reaction-diffusion type
by: A. N. Stanzhitskij, et al.
Published: (2016)
by: A. N. Stanzhitskij, et al.
Published: (2016)
Singularities of Solutions of One Class of Equations of Continuum Mechanics
by: Il'man, V. M., et al.
Published: (2003)
by: Il'man, V. M., et al.
Published: (2003)
Certain theorems on stabilization of the Cauchy problem solutions for parabolic Shilovian systems in the classes of generalized functions
by: Gorodetsky, V. V., et al.
Published: (1987)
by: Gorodetsky, V. V., et al.
Published: (1987)
On the fundamental solution of the Cauchy problem for Kolmogorov systems of the second order
by: H. P. Malytska, et al.
Published: (2018)
by: H. P. Malytska, et al.
Published: (2018)
On the fundamental solution of the Cauchy problem for
Kolmogorov systems of the second order
by: Burtnyak, I. V., et al.
Published: (2018)
by: Burtnyak, I. V., et al.
Published: (2018)
Theorems on the existence and nonexistence of solutions of the Cauchy problem for degenerate parabolic equations with nonlocal source
by: Afanaseva, N. V., et al.
Published: (2005)
by: Afanaseva, N. V., et al.
Published: (2005)
Uniqueness of solutions of mixed problems and the Cauchy problem for parabolic equation of high order with nonrestricted coef¬ficients
by: Akulov , V. F., et al.
Published: (1992)
by: Akulov , V. F., et al.
Published: (1992)
On the approximate solutions of one abstract Cauchy problem
by: V. V. Horodetskyi, et al.
Published: (2019)
by: V. V. Horodetskyi, et al.
Published: (2019)
Theorem on Closure and the Criterion of Compactness for the Classes of Solutions of the Beltrami Equations
by: T. V. Lomako
Published: (2013)
by: T. V. Lomako
Published: (2013)
Theorem on Closure and the Criterion of Compactness for the Classes of Solutions of the Beltrami Equations
by: Lomako, T.V., et al.
Published: (2013)
by: Lomako, T.V., et al.
Published: (2013)
Similar Items
-
Classical fundamental solutions of the Cauchy problem for ultraparabolic Kolmogorov type equations with two groups of spatial variables
by: S. D. Ivasyshen, et al.
Published: (2016) -
On classical fundamental solutions of the Cauchy problem for ultraparabolic equations of Kolmogorov type with two groups of spatial variables
by: S. D. Ivasyshen, et al.
Published: (2016) -
Properties of fundamental solutions, theorems on integral representations of solutions and correct solvability of the Cauchy problem for ultraparabolic Kolmogorov-type equations with two groups of spatial variables of degeneration
by: S. D. Ivasyshen, et al.
Published: (2018) -
Classical fundamental solution of the Cauchy problem for ultraparabolic Kolmogorov-type equations with two groups of spatial variables of degeneration. I
by: S. D. Ivasyshen, et al.
Published: (2017) -
Classical fundamental solution of the Cauchy problem for ultraparabolic Kolmogorov-type equations with two groups of spatial variables of degeneration. II
by: S. D. Ivasyshen, et al.
Published: (2017)