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

^*Autore corrispondente per questo lavoro

University of Bari

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

Abstract

In this work we consider differential equations of the type\r\n$$u^{(k)} = f (u),$$\r\nand 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	Inglese
pagine (da-a)	1-29
Numero di pagine	29
Rivista	Mathematics In Engineering
Volume	3
Numero di pubblicazione	5
DOI	https://doi.org/10.3934/mine.2021041
Stato di pubblicazione	Pubblicato - 2021

All Science Journal Classification (ASJC) codes

Analisi
Fisica Matematica
Matematica Applicata

Keywords

Discontinuous differential equations
Extinction profile
Finite time extinction
Oscillations
Periodic solutions

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10.3934/mine.2021041

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

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AU - D'Ambrosio, Lorenzo

AU - Gallo, Marco

AU - Pugliese, Alessandro

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AB - In this work we consider differential equations of the type\r\n$$u^{(k)} = f (u),$$\r\nand 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

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JF - Mathematics In Engineering

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A note on the Kuramoto-Sivashinsky equation with discontinuity

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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