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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| Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 262; no. 6; pp. 844 - 854 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
16.04.2022
Springer Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 1072-3374 1573-8795 1573-8795 |
| DOI | 10.1007/s10958-022-05863-3 |
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| Abstract | 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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| AbstractList | 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. 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. Keywords and phrases: Kuramoto-Sivashinsky equation, boundary-value problem, equilibrium, stability, Galerkin method, computer analysis. AMS Subject Classification: 37L10, 37L25, 37L65 |
| Audience | Academic |
| Author | Sekatskaya, A. V. |
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| Cites_doi | 10.1007/s10958-015-2438-x 10.1016/j.physd.2013.04.011 10.1134/S1054660X0903030X 10.1016/j.aml.2011.10.026 10.18255/1818-1015-2017-5-615-628 10.1137/0149039 10.1016/0167-2789(85)90009-0 10.1116/1.575561 10.1016/j.physleta.2014.11.015 10.1016/0167-2789(85)90056-9 10.18255/1818-1015-2018-1-92-101 10.1007/978-3-642-69689-3 |
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| Keywords | computer analysis 37L25 Kuramoto–Sivashinsky equation Galerkin method equilibrium boundary-value problem stability 37L10 37L65 |
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| References | Armbruster, Guckenheimer, Holmes (CR1) 1989; 3 Barker, Johnson, Noble, Zumbrun (CR2) 2012; 5 Kulikov, Kulikov (CR13) 2015; 4 Kulikov, Kulikov (CR14) 2018; 1 CR16 Emelyanov (CR5) 2009; 3 Kulikov, Kulikov (CR11) 2014; 3 CR20 Sekatskaya (CR18) 2017; 5 Nicolaenko, Scheurer, Temam (CR17) 1985; 12 Bradley, Harper (CR4) 1988; 4 Kudryashov, Ryabov, Fedyanin (CR8) 2012; 24 Kulikov, Kulikov (CR12) 2015; 6 Kulikov, Kulikov (CR10) 2012; 52 Sivashinsky (CR19) 1985; 2 Emelyanov (CR6) 2010; 74 Barker, Johnson, Noble, Rodrigues, Zumbrun (CR3) 2013; 25 Kudryashov, Ryabov, Strikhanov (CR9) 2010; 2 Gelfand, Bradley (CR7) 2015; 4 Kulikov, Kulikov, Rudyi (CR15) 2011; 4 D Armbruster (5863_CR1) 1989; 3 AN Kulikov (5863_CR10) 2012; 52 AN Kulikov (5863_CR11) 2014; 3 R Bradley (5863_CR4) 1988; 4 NA Kudryashov (5863_CR9) 2010; 2 VM Emelyanov (5863_CR6) 2010; 74 B Barker (5863_CR3) 2013; 25 NA Kudryashov (5863_CR8) 2012; 24 B Barker (5863_CR2) 2012; 5 MP Gelfand (5863_CR7) 2015; 4 BI Emelyanov (5863_CR5) 2009; 3 5863_CR16 GI Sivashinsky (5863_CR19) 1985; 2 5863_CR20 AN Kulikov (5863_CR14) 2018; 1 AN Kulikov (5863_CR13) 2015; 4 AN Kulikov (5863_CR15) 2011; 4 B Nicolaenko (5863_CR17) 1985; 12 AV Sekatskaya (5863_CR18) 2017; 5 AN Kulikov (5863_CR12) 2015; 6 |
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| SubjectTerms | Analysis Boundary conditions Boundary value problems Chemical reaction, Rate of Galerkin method Mathematics Mathematics and Statistics |
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| Title | Second-Kind Equilibrium States of the Kuramoto–Sivashinsky Equation with Homogeneous Neumann Boundary Conditions |
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