Dispersive and diffusive limits for Ostrovsky-Hunter type equations. (English) Zbl 1330.35082
Summary: We consider the equation
\[
\partial_x(\partial_tu+\partial_xf(u)-\beta\partial_{xxx}^3u)=\gamma u,
\]
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.
MSC:
| 35G25 | Initial value problems for nonlinear higher-order PDEs |
| 35L65 | Hyperbolic conservation laws |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Software:
PSEUDOReferences:
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