A singular limit problem for conservation laws related to the Kawahara-Korteweg-de Vries equation | Zendy

Giuseppe Maria Coclite | Zendy; Lorenzo di Ruvo | Zendy

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A singular limit problem for conservation laws related to the Kawahara-Korteweg-de Vries equation

Author(s) -

Giuseppe Maria Coclite,

Lorenzo di Ruvo

Publication year - 2016

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2016.11.281

Subject(s) - korteweg–de vries equation , limit (mathematics) , burgers' equation , conservation law , mathematics , compact space , dispersive partial differential equation , a priori and a posteriori , mathematical analysis , nonlinear system , zero (linguistics) , dispersion (optics) , peakon , mathematical physics , physics , partial differential equation , integrable system , philosophy , linguistics , epistemology , quantum mechanics , optics

WeconsidertheKawahara-Korteweg-deVriesequation,whichcon- tains nonlinear dispersive effects. We prove that as the dispersion 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

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