The generalized BBM-Burger equations with non-linear dissipative term: existence and convergence results

A LDG method for the fourth-order NLS equation

“…In this paper, we investigate the asymptotic behavior of the solution for the 4- There are only a few numerical works in the literature to solve the 4-order BBM-Burgers equation [1][2][3][4][5]. We develop a class of local discontinuous Galerkin (LDG) methods for this nonlinear BBM-Burgers equation (2).…”

Global asymptotic stability of the rarefaction waves to the Cauchy problem for the generalized Rosenau–Korteweg–de Vries–Burgers equation

“…There are many results concerning the existence and time-decay properties of solutions, the stability of nonlinear waves (that is, rarefaction waves, shock waves (travelling wave), viscous contact waves and and multiwave pattern of rarefaction waves and viscous contact waves) and the other mathematical structure of the models (1.2)-(1.10) (and, (1.15) and (1.16) in Remark 1.3) (for the related works, see Amick-Bona-Schonbek [2], Andreiev-Egorova-Lange-Teschl [3], Benjamin-Bona-Mahony [4], Bona-Schonbek [5], Bona-Rajopadhye-Schonbek [6], Duan-Fan-Kim-Xie [7], Duan-Zhao [8], Egorova-Grunert-Teschl [9], Egorova-Teschl [10], Harabetian [11], Hattori-Nishihara [13], Il'in-Oleȋnik [15], Kondo-Webler [17]- [20], Matsumura-Nishihara [24]- [26], Matsumura-Yoshida [27], [28], Mei [29], [30], Mei-Schmeiser [31], Naumkin [32], Nishihara-Rajopadhye [33], Osher-Ralston [34], Peregrine [35], Rajopadhye [36], Rashindinia-Nikan-Khoddam [37], Ruan-Gao-Chen [38], Wang [39], Wang-Zhu [40], Xu-Li [41], Yin-Zhao-Kim [42], Yoshida [43]- [53], Zhao-Xuan [54] and so on).…”