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.
D'Ambrosio, L., Gallo, M., Pugliese, A., A note on the Kuramoto-Sivashinsky equation with discontinuity, <<MATHEMATICS IN ENGINEERING>>, 2021; 3 (5): 1-29. [doi:10.3934/mine.2021041] [https://hdl.handle.net/10807/228864]
A note on the Kuramoto-Sivashinsky equation with discontinuity
Gallo, Marco;
2021
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.
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