Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417340 | Journal of Mathematical Analysis and Applications | 2016 | 40 Pages |
Abstract
The paper discusses initial value problem of a Korteweg-de Vries type of fifth-order equationwt+wxxxâwxxxxxââj=1najwjwx=0,w(x,0)=w0(x) posed on a periodic domain xâ[0,2Ï] with periodic boundary conditions wix(0,t)=wix(2Ï,t), i=0,2,3,4 and an L2-stabilizing feedback control law wx(2Ï,t)=αwx(0,t)+(1âα)wxxx(0,t) where n is a fixed positive integer, aj, j=1,2,â¯,n, α are real constants, and |α|<1. It is shown that for w0(x)âHα1(0,2Ï) with the boundary conditions described above, the problem is locally well-posed for wâC([0,T];Hα1(0,2Ï)) with a conserved volume of w, [w]=â«02Ïw(x,t)dx. Moreover, the solution with small initial condition exists globally and approaches to [w0(x)]/(2Ï) as tâ+â.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Guangyue Gao, Shu-Ming Sun,