Global existence and bounded estimate of solutions of the BBM-Burgers equation

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).…”

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

“…There are many results concerning with the mathematical structure, such as the global existence and time-decay properties of solutions, of the generalized Benjamin-Bona-Mahony-Burgers equation with the dissipative terms (see , [22], [23], [24], Wang [49], Xu-Li [51] Zhao-Xuan [64] and so on). The model (1.1) is closely related to the following Benjamin-Bona-Mahony-Burgers equation…”