We consider the equation \begin{equation*} \px(\pt u+\px f(u)-\beta \pxxx u)=\gamma u, \end{equation*} that includes the short pulse, the Ostrovsky-Hunter, and the Korteweg-deVries ones. We consider here the asymptotic behavior as $\gamma\to 0$. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the $L^p$ setting.
Dispersive and Diffusive limits for Ostrovsky-Hunter type equations / Coclite, Giuseppe Maria; di Ruvo, L.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 22:6(2015), pp. 1733-1763. [10.1007/s00030-015-0342-1]
Dispersive and Diffusive limits for Ostrovsky-Hunter type equations
COCLITE, Giuseppe Maria;
2015-01-01
Abstract
We consider the equation \begin{equation*} \px(\pt u+\px f(u)-\beta \pxxx u)=\gamma u, \end{equation*} that includes the short pulse, the Ostrovsky-Hunter, and the Korteweg-deVries ones. We consider here the asymptotic behavior as $\gamma\to 0$. 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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