TY - JOUR
T1 - Asymptotic behavior of solutions to the Rosenau-Burgers equation with a periodic initial boundary
AU - Liu, Liping
AU - Mei, Ming
AU - Wong, Yau Shu
PY - 2007/10/15
Y1 - 2007/10/15
N2 - This study focuses on the Rosenau-Burgers equation ut + ux x x x t - α ux x + f (u)x = 0 with a periodic initial boundary condition. It is proved that with smooth initial value the global solution uniquely exists. Furthermore, for α > 0, the global solution converges time asymptotically to the average of the initial value in an exponential form, and the convergence rate is optimal; while for α = 0, the unique solution oscillates around the initial average all the time. Finally, the numerical simulations are reported to confirm the theoretical results. © 2006 Elsevier Ltd. All rights reserved.
AB - This study focuses on the Rosenau-Burgers equation ut + ux x x x t - α ux x + f (u)x = 0 with a periodic initial boundary condition. It is proved that with smooth initial value the global solution uniquely exists. Furthermore, for α > 0, the global solution converges time asymptotically to the average of the initial value in an exponential form, and the convergence rate is optimal; while for α = 0, the unique solution oscillates around the initial average all the time. Finally, the numerical simulations are reported to confirm the theoretical results. © 2006 Elsevier Ltd. All rights reserved.
KW - Convergence
KW - Oscillation
KW - Periodic boundary condition
KW - Rosenau-Burgers equation
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U2 - 10.1016/j.na.2006.08.047
DO - 10.1016/j.na.2006.08.047
M3 - Article
SN - 0362-546X
VL - 67
SP - 2527
EP - 2539
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 8
ER -