Cover Image

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

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...

Full description

Saved in:

Bibliographic Details
Date:	2010
Main Authors:	Ivasyshen, S. D., Litovchenko, V. A., Івасишен, С. Д., Літовченко, В. А.
Format:	Article
Language:	Ukrainian English
Published:	Institute of Mathematics, NAS of Ukraine 2010
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/2958
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Cauchy problem for one class of degenerate parabolic equations of Kolmogorov type with positive genus
by: Ivasyshen, S. D., et al.
Published: (2009)

Fundamental solutions of the Cauchy problem for some degenerate parabolic equations of the Kolmogorov type
by: Ivasyshen, S. D., et al.
Published: (2011)

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)

The fundamental solution of the Cauchy problem for degenerated parabolic Kolmogorov type equations of arbitrary order
by: S. D. Ivasyshen, et al.
Published: (2019)

Cauchy problem for degenerate parabolic systems of Kolmogorov type in weighted Lebesgue spaces
by: V. A. Litovchenko, et al.
Published: (2014)

Fundamental solution of the Cauchy problem for a class of degenerate parabolic pseudo-differential equations
by: V. A. Litovchenko
Published: (2013)

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)

Complete Solvability of the Cauchy Problem for Petrovskii Parabolic Equations in S-Type Spaces
by: Litovchenko, V. A., et al.
Published: (2002)

Boundary values of smooth solutions of degenerate parabolic systems of the Kolmogorov type
by: V. A. Litovchenko, et al.
Published: (2015)

Boundary values of smooth solutions of Kolmogorov degenerate parabolic equations (p, h)
by: V. A. Litovchenko
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 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)

Kolmogorov’s equation for the Cauchy problem’s solution of one class of linear evolutional equations
by: Mestechkina, T. M., et al.
Published: (1987)

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)

On the Cauchy Problem for $\mathop {2b}\limits^ \to$ -Parabolic Systems with Growing Coefficients
by: Ivasyshen, S. D., et al.
Published: (2000)

Fundamental solution of the Cauchy problem for one parabolic equation with increasing lowest coefficients
by: S. D. Ivasyshen, et al.
Published: (2014)

One method for the investigation of the fundamental solution of the Cauchy problem for parabolic systems
by: Litovchenko, V. A., 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)

Fundamental solution of the Cauchy problem for the Shilov-type parabolic systems with coefficients of bounded smoothness
by: Litovchenko, V. A., et al.
Published: (2017)

Properties of the fundamental solutions and uniqueness theorems for the solutions of the Cauchy problem for one class of ultraparabolic equations
by: Ivasyshen, S. D., et al.
Published: (1998)

Asymptotic behaviour of the solution of Cauchy’s problem for stochastic equation of parabolic type
by: Dorogovtsev , A. Ya., et al.
Published: (1988)

Cauchy Problem for Nonuniformly Parabolic Equations with Degeneracy
by: Pukalskyi, I. D., et al.
Published: (2003)

Cauchy problem for one class of pseudodifferential systems with entire analytic symbols
by: Litovchenko, V. A., et al.
Published: (2006)

Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. I
by: Romanyuk, V. S., et al.
Published: (2001)

Estimates of the Kolmogorov Widths of Classes of Analytic Functions Representable by Cauchy-Type Integrals. II
by: Romanyuk, V. S., et al.
Published: (2001)

On a generalization of a Cauchy problem for singular parabolic type evolution equations
by: V. V. Horodetskyi, et al.
Published: (2016)

Correct Solvability of the Cauchy Problem for One Equation of Integral Form
by: Litovchenko, V. A., et al.
Published: (2004)

Fundamental solution of the Cauchy problem for the Shilov-type parabolic systems with coefficients of bounded smoothness
by: V. A. Litovchenko, et al.
Published: (2017)

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)

In bifurcated solution of the Cauchy problem for one class of parabolic systems
by: Lenуuk, M. P., et al.
Published: (1970)

Nonlocal Dirichlet problem for linear parabolic equations with degeneration
by: Pukalskyi, I. D., et al.
Published: (2007)

Nonlocal Neumann problem for a degenerate parabolic equation
by: Pukalskyi, I. D., et al.
Published: (1999)

On the behavior of solutions of the Cauchy problem for a degenerate parabolic equation with source in the case where the initial function slowly vanishes
by: Martynenko, A. V., et al.
Published: (2012)

Geometric Constructions in the Class of Busemann Nonpositively Curved Spaces
by: Andreev, P.D.
Published: (2009)

On stabilization of solutions of the cauchy problem for parabolic equations on the nets
by: Denisov, V.
Published: (2000)

Nonlocal Inverse Problem for a Parabolic Equation with Degeneration
by: N. M. Huzyk
Published: (2013)

Nonlocal multipoint in time problem for parabolic equations with degeneration
by: I. D. Pukalskyi, et al.
Published: (2017)

Nonlocal Inverse Problem for a Parabolic Equation with Degeneration
by: Huzyk, N. M., et al.
Published: (2013)