Mathematics in Engineering

2021, Issue 5: 1-29. doi: 10.3934/mine.2021041
Research article Special Issues

A note on the Kuramoto-Sivashinsky equation with discontinuity

• Received: 25 July 2020 Accepted: 09 September 2020 Published: 22 October 2020
• 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 $-u^{(4)} = sgn(u)$, 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.

Citation: Lorenzo D'Ambrosio, Marco Gallo, Alessandro Pugliese. A note on the Kuramoto-Sivashinsky equation with discontinuity[J]. Mathematics in Engineering, 2021, 3(5): 1-29. doi: 10.3934/mine.2021041

Related Papers:

• 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 $-u^{(4)} = sgn(u)$, 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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沈阳化工大学材料科学与工程学院 沈阳 110142

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