Details

Autor(en) / Beteiligte

• Gao, Guangyue
• Sun, Shu-Ming

Titel

A Korteweg–de Vries type of fifth-order equations on a finite domain with point dissipation

Ist Teil von

• Journal of mathematical analysis and applications, 2016-06, Vol.438 (1), p.200-239

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2016

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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→+∞.