On Squeezing and Flow of Energy for Nonlinear Wave Equations

@inproceedings{Kuksin1995OnSA,
  title={On Squeezing and Flow of Energy for Nonlinear Wave Equations},
  author={Sergej B. Kuksin},
  year={1995}
}
  • Sergej B. Kuksin
  • Published 1995
Geometric and Functional Analysis (GAFA), vol.5 (1995) Abstract. We study the nonlinear wave equation ü − δ△u + f(u) = 0 under n-dimensional periodic boundary conditions (n=1, 2, 3) in a Sobolev phase-space Hs = Hs × Hs−1(Tn) = {(u, u̇)(x)}. In [8] we interpreted the “energy transition to higher frequencies” problem for this (and similar) equations as a squeezing: time-t flow maps of the equation with large t “squeeze” r-balls in Hs to narrow cylinders formed by vector-functions such that the… CONTINUE READING