Averaging, Conley Index Continuation and Recurrent Dynamics in Almost-periodic Parabolic Equations

  • Published 2004
We study a non-autonomous parabolic equation with almost-periodic, rapidly oscillating principal part and nonlinear interactions. We associate to the equation a skew-product semiflow and, for a special class of nonlinearities, we define the Conley index of an isolated invariant set. As the frequency of the oscillations tends to infinity, we prove that every… CONTINUE READING