News & Announcements
Links
On the Growth in Time of Sobolev Norms for TimeDependent Linear Generalized KdV-typeEquations
  
View Full Text  View/Add Comment  Download reader
KeyWord:Sobolev norms  Time dependent linear generalized KdV-type equa- tion  Fixed analytic potential
Author NameAffiliation
Chengming Cao School of Mathematical Sciences, Fudan University, Shanghai 200433, China 
Xiaoping Yuan School of Mathematical Sciences, Fudan University, Shanghai 200433, China 
Hits: 432
Download times: 577
Abstract:
      We give a detailed description in 1-D the growth of Sobolev norms for time dependent linear generalized KdV-type equations on the circle. For most initial data, the growth of Sobolev norms is polynomial in time for fixed analytic potential with admissible growth. If the initial data are given in a fixed smaller function space with more strict admissible growth conditions for V (x,t) , then the growth of previous Sobolev norms is at most logarithmic in time.