Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One
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.
2016 ◽
Vol 21
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pp. 239-259
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2009 ◽
2020 ◽
Vol 57
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pp. 68-90
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1990 ◽
Vol 84
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pp. 100-128
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2010 ◽
Vol 138
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pp. 4359-4359