Cover Image

On the Correct Solvability of One Cauchy Problem

We establish a criterion for convolutors in certain S-type spaces. Using this criterion, we prove the correct solvability (in both directions) of one Cauchy problem in these spaces.

Saved in:

Bibliographic Details
Date:	2002
Main Authors:	Litovchenko, V. A., Літовченко, В. А.
Format:	Article
Language:	Ukrainian English
Published:	Institute of Mathematics, NAS of Ukraine 2002
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/4147
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

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

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

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

One method for the investigation of the fundamental solution of the Cauchy problem for parabolic systems
by: Litovchenko, V. A., et al.
Published: (2018)

Cauchy problem with Riesz operator of fractional differentiation
by: Litovchenko, V. A., et al.
Published: (2005)

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

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)

Correct Solvability of a Nonlocal Multipoint (in Time) Problem for One Class of Evolutionary Equations
by: Horodets’kyi, V. V., et al.
Published: (2013)

Correct Solvability of a Nonlocal Multipoint (in Time) Problem for One Class of Evolutionary Equations
by: V. V. Horodetskyi, et al.
Published: (2013)

One method for the investigation of the fundamental solution of the Cauchy problem for parabolic systems
by: V. A. Litovchenko
Published: (2018)

On Stability of the Cauchy Equation on Solvable Groups
by: Faiziev, V. A., et al.
Published: (2015)

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 Stability of the Cauchy Equation on Solvable Groups
by: V. A. Faiziev, et al.
Published: (2015)

Conditions of solvability of the problem inverse to the Cauchy problem for the difference-algebraic equation
by: S. M. Chuiko, et al.
Published: (2021)

On asymptotics of solutions of one Cauchy’s problem
by: Zernov , A. E., et al.
Published: (2025)

Correctness of the Cauchy problem for trinomial higher-order operator differential equations
by: Shklyar, A. Ya., et al.
Published: (1993)

On the approximate solutions of one abstract Cauchy problem
by: V. V. Horodetskyi, et al.
Published: (2019)

Correct solvability of Solonnikov–Eidel’man parabolic initial-value problems
by: Ivasyshen, S. D., et al.
Published: (2009)

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)

Cauchy problem for a class of degenerate kolmogorov-type parabolic equations with nonpositive genus
by: Ivasyshen, S. D., et al.
Published: (2010)

Some new conditions for the solvability of the cauchy problem for systems of linear functional-differential equations
by: Dil'na, N. Z., et al.
Published: (2004)

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)

On the correct solvability of the Dirichlet problem for operator differential equations in a Banach space
by: Gorbachuk, V. M., et al.
Published: (2006)

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)

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

On one extremal problem for nonlinear Cauchy-Riemann-Beltrami systems
by: R. R. Salimov, et al.
Published: (2020)

One method for solution of the Cauchy problem for singular parabolic equations
by: Matiichuk , M. I., et al.
Published: (1992)

Modified Cauchy problem for one degenerated hyperbolic equation of the second kind
by: Urinov, A. K., et al.
Published: (2020)

On generalized Cauchy problem for one class of differential equation of infinite order
by: Horodets’kyi , V. V., et al.
Published: (2020)

Correct solvability of the difference Pade schemes for parabolic equations in Holder spaces
by: Ashyraliev, A., et al.
Published: (1992)

Modified Cauchy problem for one degenerated hyperbolic equation of the second kind
by: A. K. Urinov, et al.
Published: (2020)

On generalized Cauchy problem for one class of differential equation of infinite order
by: V. V. Horodetskyi, et al.
Published: (2020)

On the structure of the general solution and conditions of solvability of the Cauchy problem for degenerate linear systems of higher-order differential equations
by: Pafyk, S. P., et al.
Published: (2013)

Conditions for one-valued solvability of nonlinear stationary heat-conduction problems
by: Zhernovoi, Yu. V., et al.
Published: (1999)

On one proof of the classical solvability of the Hele-Shaw problem with free boundary
by: Bazalii, B. V., et al.
Published: (1998)

Fundamental solution of the Cauchy problem for (p,h) - parabolic systems with variable coefficients
by: V. A. Litovchenko
Published: (2018)

On the structure of the general solution and conditions of solvability of the Cauchy problem for degenerate linear systems of higher-order differential equations
by: S. P. Pafyk, et al.
Published: (2013)

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)

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

Characterization of the rate of convergence of one approximate method for the solution of an abstract Cauchy problem
by: Kashpirovskii, A. I., et al.
Published: (2008)