We consider the Ibragimov-Shabat 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 a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the $L^p$ setting.

A singular limit problem for the Ibragimov-Shabat equation / Coclite, Giuseppe Maria; di Ruvo, L.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 9:3(2016), pp. 661-673. [10.3934/dcdss.2016020]

A singular limit problem for the Ibragimov-Shabat equation

COCLITE, Giuseppe Maria;
2016-01-01

Abstract

We consider the Ibragimov-Shabat 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 a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the $L^p$ setting.
2016
A singular limit problem for the Ibragimov-Shabat equation / Coclite, Giuseppe Maria; di Ruvo, L.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 9:3(2016), pp. 661-673. [10.3934/dcdss.2016020]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/93895
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