TIME-DEPENDENT ATTRACTOR FOR THE OSCILLON EQUATION

We investigate the asymptotic behavior of the nonautonomous evolution problem generated by the Oscillon equation partial derivative(tt)u(x, t)+ H partial derivative(t)u(x, t) -e(-2Ht) partial derivative(xx)u(x, t) + V'(u(x, t)) = 0, (x, t) is an element of (0, 1) x R, with periodic boundary conditions, where H > 0 is the Hubble constant and V is a nonlinear potential of arbitrary polynomial growth. After constructing a suitable dynamical framework to deal with the explicit time dependence of the energy of the solution, we establish the existence of a regular global attractor A = A(t). The kernel sections A(t) have finite fractal dimension.