Cover Image

On One Nonlocal Problem with Free Boundary

We investigate group-theoretic properties of a nonlocal problem with free boundary for a degenerating quasilinear parabolic equation. We establish conditions for the invariant solvability of this problem, perform its reduction, and obtain an exact self-similar solution.

Saved in:

Bibliographic Details
Date:	2001
Main Authors:	Berezovsky, A. A., Mitropolskiy, Yu. A., Netesova, T. M., Березовский, А. А., Митропольский, Ю. А., Нетесова, Т. М.
Format:	Article
Language:	Russian English
Published:	Institute of Mathematics, NAS of Ukraine 2001
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/4312
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

Group analysis of boundary-value problems of mathematical physics
by: Netesova, T. M., et al.
Published: (1999)

On the invariance of a boundary-value problem for a nonlinear evolution equation
by: Netesova, A. M., et al.
Published: (1998)

Problems with free boundaries and nonlocal problems for nonlinear parabolic equations
by: Berezovsky, A. A., et al.
Published: (1997)

Space-time localization in problems with free boundaries for a nonlinear second-order equation
by: Berezovsky, A. A., et al.
Published: (1996)

Finite-Time Stabilization in Problems with Free Boundary for Nonlinear Equations in Media with Fractal Geometry
by: Berezovsky, A. A., et al.
Published: (2005)

Problems with free boundaries for the nonlinear evolution equation in problems of metallurgy, medicine, ecology
by: Mitropolsky , Yu. A., et al.
Published: (1992)

Об одной нелокальной задаче со свободной границей
by: Березовский, А.А., et al.
Published: (2001)

Nonlinear nonlocal problems for a parabolic equation in a two-dimensional domain
by: Berezovsky, A. A., et al.
Published: (1997)

Problem with nonlocal condition on the free boundary
by: Takhirov, Zh. O., et al.
Published: (2012)

Problems with free boundaries for nonlinear parabolic equations
by: Berezovsky, A. A., et al.
Published: (1997)

On a nonlocal problem for a parabolic equation
by: Berezansky, Yu. M., et al.
Published: (1995)

One-dimensional problems with free boundaries in ecology
by: Berezovs'kyi, M. A., et al.
Published: (1997)

Stabilization for a finite time in problems with free boundary for some classes of nonlinear second-order equations
by: Berezansky, Yu. M., et al.
Published: (1999)

Analyticity of a free boundary in one problem of axisymmetric flow
by: Minenko, A. S., et al.
Published: (1998)

One version of the Linearized theory of nonstationary boundary-value problems with free boundary
by: Lukovsky, I. O., et al.
Published: (1996)

Boundary-value problems for the heat conduction equation with a fractional derivative in the boundary conditions. Difference methods for numerical realization of these problems
by: Berezovsky, A. A., et al.
Published: (1993)

Групповой анализ краевых задач математической физики
by: Нетесова, Т.М.
Published: (1999)

On a Nonlocal Boundary-Value Problem for Systems of Impulsive Hyperbolic Equations
by: Assanova, A. T., et al.
Published: (2013)

On one problem with free boundary for a nonlinear system
by: Bazalii, B. V., et al.
Published: (1996)

One-Sided Nonlocal Boundary-Value Problem for Singular Parabolic Equations
by: Pukalskyi, I. D., et al.
Published: (2001)

School-seminar “Nonlinear boundary value problems of mathematical physics and their applications”
by: Samoilenko, A. M., et al.
Published: (1990)

Nonlocal parabolic boundary-value problem
by: Matychuk, M. I., et al.
Published: (1996)

On the variational statement of one boundary-value problem with free interface
by: Timokha, A., et al.
Published: (2023)

On the construction of an asymptotic solution of a perturbed Bretherton equation
by: Mitropolskiy, Yu. A., et al.
Published: (1998)

On the 90th Anniversary of the Birth of Academician N.N. Bogolyubov
by: Mitropolskiy, Yu. A., et al.
Published: (1999)

On construction of asymptotic solution of the perturbed Klein-Gordon equation
by: Mitropolskiy, Yu. A., et al.
Published: (1995)

Approximate solution of the Fokker-Planck-Kolmogorov equation
by: Mitropolskiy, Yu. A., et al.
Published: (1995)

On the Scientific, Pedagogic, and Public Activities of Academician Mikhail Alekseevich Lavrent'ev at the Ukrainian Academy of Sciences (1939–1949) (on the 100th Anniversary of the Birth of M. A. Lavrent'ev)
by: Mitropolskiy, Yu. A., et al.
Published: (2000)

Mark Grigor'evich Krein
by: Mitropolskiy, Yu. A., et al.
Published: (1994)

Об одной нелокальной задаче для параболического уравнения
by: Митропольский, Ю.А., et al.
Published: (1995)

Nonlocal boundary-value problem for parabolic equations
by: Zadorozhna, N. M., et al.
Published: (1994)

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

Well-Posed Solvability of a Nonlocal Boundary-Value Problem for the Systems of Hyperbolic Equations with Impulsive Effects
by: Assanova, A. T., et al.
Published: (2015)

Эквивалентная линеаризация систем с распределенными параметрами
by: Митропольский, Ю.А., et al.
Published: (1986)

Стабилизация за конечное время в задачах со свободной границей для нелинейных уравнений в средах с фрактальной геометрией
by: Березовский, А.А., et al.
Published: (2005)

Нелинейные нелокальные задачи для параболического уравнения в двумерной области
by: Митропольский, Ю.А., et al.
Published: (1997)

Initial-boundary-value problem for a semilinear parabolic equation with nonlinear nonlocal boundary conditions
by: Gladkov, A. L., et al.
Published: (2016)

Nonlocal parabolic boundary value problems with features
by: I. D. Pukalskyi, et al.
Published: (2013)

On the unique solvability of a nonlocal boundary-value problem for systems of loaded hyperbolic equations with impulsive actions
by: Assanova, A. T., et al.
Published: (2017)

On solvability of nonlocal boundary value problems for certain sets of evolutionary differential equations
by: Malovichko , V. A., et al.
Published: (2025)