We consider the modified Kawahara equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to the discontinuous weak solutions of the 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.
Convergence results related to the modified Kawahara equation / Coclite, Giuseppe Maria; DI RUVO, L.. - In: BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA. - ISSN 1972-6724. - 8:4(2016), pp. 265-286. [10.1007/s40574-015-0043-z]
Convergence results related to the modified Kawahara equation
COCLITE, Giuseppe Maria;
2016-01-01
Abstract
We consider the modified Kawahara equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to the discontinuous weak solutions of the 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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
