Article ID Journal Published Year Pages File Type
6417340 Journal of Mathematical Analysis and Applications 2016 40 Pages PDF
Abstract

The paper discusses initial value problem of a Korteweg-de Vries type of fifth-order equationwt+wxxx−wxxxxx−∑j=1najwjwx=0,w(x,0)=w0(x) posed on a periodic domain x∈[0,2π] with periodic boundary conditions wix(0,t)=wix(2π,t), i=0,2,3,4 and an L2-stabilizing feedback control law wx(2π,t)=αwx(0,t)+(1−α)wxxx(0,t) where n is a fixed positive integer, aj, j=1,2,⋯,n, α are real constants, and |α|<1. It is shown that for w0(x)∈Hα1(0,2π) with the boundary conditions described above, the problem is locally well-posed for w∈C([0,T];Hα1(0,2π)) with a conserved volume of w, [w]=∫02πw(x,t)dx. Moreover, the solution with small initial condition exists globally and approaches to [w0(x)]/(2π) as t→+∞.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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