Time-dependent attractor for the Oscillon equation
Time-dependent attractor for the Oscillon equation
We investigate the asymptotic behavior of the nonautonomous evolution problem generated bythe Oscillon equation ∂ tt $u(x,t) +H $ ∂ t$ u(x,t) -\e^{-2Ht}$ ∂ xx $ u(x,t) +V'(u(x,t)) =0, \quad (x,t)\in (0,1) \times \R,$with periodic boundary conditions, where $H>0$ is the Hubbleconstant and $V$ is a nonlinear potential of arbitrary …