TY - JOUR
T1 - A note on the Kuramoto-Sivashinsky equation with discontinuity
AU - D'Ambrosio, Lorenzo
AU - Gallo, Marco
AU - Pugliese, Alessandro
PY - 2021
Y1 - 2021
N2 - 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.
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
UR - https://publicatt.unicatt.it/handle/10807/228864
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85141173498&origin=inward
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85141173498&origin=inward
U2 - 10.3934/mine.2021041
DO - 10.3934/mine.2021041
M3 - Article
SN - 2640-3501
VL - 3
SP - 1
EP - 29
JO - Mathematics In Engineering
JF - Mathematics In Engineering
IS - 5
ER -