Second-Kind Equilibrium States of the Kuramoto–Sivashinsky Equation with Homogeneous Neumann Boundary Conditions

In this paper, we consider the boundary-value problem for the Kuramoto–Sivashinsky equation with homogeneous Neumann conditions. The problem on the existence and stability of second-kind equilibrium states was studied in two ways: by the Galerkin method and by methods of the modern theory of infinit...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 262; no. 6; pp. 844 - 854
Main Author Sekatskaya, A. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 16.04.2022
Springer
Springer Nature B.V
Subjects
Analysis
Boundary conditions
Boundary value problems
Chemical reaction, Rate of
Galerkin method
Mathematics
Mathematics and Statistics
computer analysis
37L25
Kuramoto–Sivashinsky equation
Galerkin method
equilibrium
boundary-value problem
stability
37L10
37L65
Online AccessGet full text
ISSN1072-3374
1573-8795
1573-8795
DOI10.1007/s10958-022-05863-3

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Summary:In this paper, we consider the boundary-value problem for the Kuramoto–Sivashinsky equation with homogeneous Neumann conditions. The problem on the existence and stability of second-kind equilibrium states was studied in two ways: by the Galerkin method and by methods of the modern theory of infinite-dimensional dynamical systems. Some differences in results obtained are indicated.
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ISSN:1072-3374
1573-8795
1573-8795
DOI:10.1007/s10958-022-05863-3