Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10224161 | Journal of Mathematical Analysis and Applications | 2018 | 22 Pages |
Abstract
This paper studies the fifth-order Korteweg-de Veries equation posed on finite interval(0.1){âtuââx5u+ε1âx4u+κ1âx3uâε2âx2u+κ2âxu+ε3u+uâxu=0,xâ(0,1),tâ¥0,u(x,0)=Ï(x),xâ(0,1),u(0,t)=u(1,t)=âxu(0,t)=âxu(1,t)=0,âx2u(1,t)=ξâx2u(0,t),tâ¥0. Firstly, we establish smoothing effect of Kato type for the fifth-order Korteweg-de Veries equation posed on finite interval; Secondly, we show that the closed loop system (0.1) is globally well-posed in the space Hs(0,1) for sâ[0,5]; Lastly, we prove that the solution of the closed loop system (0.1) is exponentially decay in the space Hs(0,1) for sâ[0,5].
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xiangqing Zhao, Xiaoying Zhang, Hongyinping Feng,