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.
A singular limit problem for conservation laws related to the Kawahara-Korteweg-de Vries equation / Coclite, Giuseppe Maria; Di RUVO, L.. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - 11:2(2016), pp. 281-300. [10.3934/nhm.2016.11.281]
A singular limit problem for conservation laws related to the Kawahara-Korteweg-de Vries equation
COCLITE, Giuseppe Maria;
2016-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
