Fixed points of a destabilized Kuramoto-Sivashinsky equation

Ferenc A. Bartha; Warwick Tucker

doi:10.1016/j.amc.2015.05.082

Fixed points of a destabilized Kuramoto-Sivashinsky equation

Ferenc A. Bartha, Warwick Tucker

Research output: Contribution to journal › Article › Research › peer-review

5 Citations (Scopus)

Abstract

We consider the family of destabilized Kuramoto-Sivashinsky equations in one spatial dimension u_t + νu_xxxx + βu_xx + γuu_x = αu for α, ν ≥ 0 and β, γ ∈ ℝ. For certain parameter values, shock-like stationary solutions have been numerically observed. In this work we verify the existence of several such solutions using the framework of self-consistent bounds and validated numerics.

Original language	English
Pages (from-to)	339-349
Number of pages	11
Journal	Applied Mathematics and Computation
Volume	266
DOIs	https://doi.org/10.1016/j.amc.2015.05.082
Publication status	Published - 1 Sep 2015
Externally published	Yes

Keywords

Boundary value problem
Galerkin projection
Interval arithmetic
Kuramoto-Sivashinsky equations
Rigorous computations
Self-consistent bounds

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10.1016/j.amc.2015.05.082

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abstract = "We consider the family of destabilized Kuramoto-Sivashinsky equations in one spatial dimension ut + νuxxxx + βuxx + γuux = αu for α, ν ≥ 0 and β, γ ∈ ℝ. For certain parameter values, shock-like stationary solutions have been numerically observed. In this work we verify the existence of several such solutions using the framework of self-consistent bounds and validated numerics.",

keywords = "Boundary value problem, Galerkin projection, Interval arithmetic, Kuramoto-Sivashinsky equations, Rigorous computations, Self-consistent bounds",

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AB - We consider the family of destabilized Kuramoto-Sivashinsky equations in one spatial dimension ut + νuxxxx + βuxx + γuux = αu for α, ν ≥ 0 and β, γ ∈ ℝ. For certain parameter values, shock-like stationary solutions have been numerically observed. In this work we verify the existence of several such solutions using the framework of self-consistent bounds and validated numerics.

KW - Boundary value problem

KW - Galerkin projection

KW - Interval arithmetic

KW - Kuramoto-Sivashinsky equations

KW - Rigorous computations

KW - Self-consistent bounds

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DO - 10.1016/j.amc.2015.05.082

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VL - 266

SP - 339

EP - 349

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -

Fixed points of a destabilized Kuramoto-Sivashinsky equation

Abstract

Keywords

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