In this work we consider differential equations of the type $$pm, u^{(k)}=f(u),$$ and study the extinction profile of their solutions. Emphasis is placed on the special case $-u^{(4)}=sign(u)$, 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.
A note on the Kuramoto-Sivashinsky equation with discontinuity
Lorenzo D'Ambrosio;
2021-01-01
Abstract
In this work we consider differential equations of the type $$pm, u^{(k)}=f(u),$$ and study the extinction profile of their solutions. Emphasis is placed on the special case $-u^{(4)}=sign(u)$, 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.File in questo prodotto:
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