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Mathematics in Engineering

2021, Volume 3, Issue 5: 1-29. doi: 10.3934/mine.2021041
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A note on the Kuramoto-Sivashinsky equation with discontinuity

  • Dipartimento di Matematica, Università degli Studi di Bari, via E. Orabona, 4, I-70125 Bari, Italy
  • 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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