A note on the Kuramoto-Sivashinsky equation with discontinuity

Lorenzo D'Ambrosio; Marco Gallo; Alessandro Pugliese

doi:10.3934/mine.2021041

A note on the Kuramoto-Sivashinsky equation with discontinuity

Lorenzo D'Ambrosio, Marco Gallo, Alessandro Pugliese

University of Bari

Risultato della ricerca: Contributo in rivista › Articolo in rivista › peer review

Abstract

In this work we consider differential equations of the type $$u^{(k)} = f (u),$$ and study the extinction profile of their solutions. Emphasis is placed on the special case $-u^{(4)} = \sgn(u)$, which is related to the Kuramoto-Sivashinsky equation. In this case we describe in more detail the extinction phenomenon and prove a conjecture by Galaktionov and Svirshchevskii.

Lingua originale	English
pagine (da-a)	1-29
Numero di pagine	29
Rivista	Mathematics In Engineering
Volume	3
DOI	https://doi.org/10.3934/mine.2021041
Stato di pubblicazione	Pubblicato - 2021

Keywords

Discontinuous differential equations
Extinction profile
Finite time extinction
Oscillations
Periodic solutions

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10.3934/mine.2021041

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keywords = "Discontinuous differential equations, Extinction profile, Finite time extinction, Oscillations, Periodic solutions, Discontinuous differential equations, Extinction profile, Finite time extinction, Oscillations, Periodic solutions",

author = "Lorenzo D'Ambrosio and Marco Gallo and Alessandro Pugliese",

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AU - D'Ambrosio, Lorenzo

AU - Gallo, Marco

AU - Pugliese, Alessandro

PY - 2021

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N2 - In this work we consider differential equations of the type $$u^{(k)} = f (u),$$ and study the extinction profile of their solutions. Emphasis is placed on the special case $-u^{(4)} = \sgn(u)$, which is related to the Kuramoto-Sivashinsky equation. In this case we describe in more detail the extinction phenomenon and prove a conjecture by Galaktionov and Svirshchevskii.

AB - In this work we consider differential equations of the type $$u^{(k)} = f (u),$$ and study the extinction profile of their solutions. Emphasis is placed on the special case $-u^{(4)} = \sgn(u)$, which is related to the Kuramoto-Sivashinsky equation. In this case we describe in more detail the extinction phenomenon and prove a conjecture by Galaktionov and Svirshchevskii.

KW - Discontinuous differential equations

KW - Extinction profile

KW - Finite time extinction

KW - Oscillations

KW - Periodic solutions

KW - Discontinuous differential equations

KW - Extinction profile

KW - Finite time extinction

KW - Oscillations

KW - Periodic solutions

UR - http://hdl.handle.net/10807/228864

UR - http://www.aimspress.com/article/10.3934/mine.2021041

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DO - 10.3934/mine.2021041

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SN - 2640-3501

VL - 3

SP - 1

EP - 29

JO - Mathematics In Engineering

JF - Mathematics In Engineering

ER -

A note on the Kuramoto-Sivashinsky equation with discontinuity

Abstract

Keywords

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