Asymptotic behavior of solutions toward the rarefaction waves to the Cauchy problem for the generalized Benjamin-Bona-Mahony-Burgers equation with dissipative term

Autor:	Yoshida, Natsumi
Rok vydání:	2021
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem with the far field condisiton for the generalized Benjamin-Bona-Mahony-Burgers equation with a fourth-order dissipative term. 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 the generalized Korteweg-de Vries-Benjamin-Bona-Mahony-Burgers equation with a fourth-order dissipative term as the former one. Comment: arXiv admin note: substantial text overlap with arXiv:2107.07874
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.06058 Zobrazit plný text záznamu View this record from Arxiv