We consider the Kuramoto-Sinelshchikov equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Burgers equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the $L^p$ setting.
Convergence of the Kuramoto-Sinelshchikov equation to the Burgers one / Coclite, Giuseppe Maria; di Ruvo, L.. - In: ACTA APPLICANDAE MATHEMATICAE. - ISSN 0167-8019. - 145:1(2016), pp. 89-113. [10.1007/s10440-016-0049-2]
Convergence of the Kuramoto-Sinelshchikov equation to the Burgers one
COCLITE, Giuseppe Maria;
2016-01-01
Abstract
We consider the Kuramoto-Sinelshchikov equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Burgers equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the $L^p$ setting.File in questo prodotto:
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