We consider the Kawahara equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solution of the dispersive equation converges to the unique entropy solution 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 equation / Coclite, Giuseppe Maria; di Ruvo, L.. - In: BULLETIN DES SCIENCES MATHEMATIQUES. - ISSN 0007-4497. - 140:3(2016), pp. 303-338. [10.1016/j.bulsci.2015.12.003]
A singular limit problem for conservation laws related to the Kawahara equation
COCLITE, Giuseppe Maria;
2016-01-01
Abstract
We consider the Kawahara equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solution of the dispersive equation converges to the unique entropy solution 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.File in questo prodotto:
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