Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One

Authors

  • Giuseppe Maria Coclite Department of Mechanics, Mathematics and Management, Polytechnic University of Bari, Via E. Orabona 4, 70125 Bari, Italy
  • Lorenzo di Ruvo Department of Mathematics, University of Bari, via E. Orabona 4, 70125 Bari, Italy

DOI:

https://doi.org/10.37256/cm.152020502

Keywords:

existence, uniqueness, stability, rosenau-korteweg-de vries-equation, korteweg-de vries equation

Abstract

The Rosenau-Korteweg-de Vries equation describes the wave-wave and wave-wall interactions. In this paper, we prove that, as the diffusion parameter is near zero, it coincides with the Korteweg-de Vries equation. The proof relies on deriving suitable a priori estimates together with an application of the Aubin-Lions Lemma.

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Published

2020-09-29

How to Cite

1.
Coclite GM, Ruvo L di. Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One. Contemp. Math. [Internet]. 2020 Sep. 29 [cited 2024 Dec. 11];1(5):365-92. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/502