We consider the Ostrovsky equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tend to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Ostrovsky-Hunter 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 Ostrovsky Equation to the Ostrovsky–Hunter One / Coclite, Giuseppe Maria; di Ruvo, L.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 256:9(2014), pp. 3245-3277. [10.1016/j.jde.2014.02.001]
Convergence of the Ostrovsky Equation to the Ostrovsky–Hunter One
COCLITE, Giuseppe Maria;
2014-01-01
Abstract
We consider the Ostrovsky equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tend to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Ostrovsky-Hunter 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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