Abstract:In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem with the far field condition for the generalized Rosenau-Korteweg-de Vries-Burgers equation. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity. We can further obtain the same global asymptotic stability of the rarefaction wave to th… Show more
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