Abstract
In this paper we compute the dynamical spectrum for time dependent scalar parabolic equations with both Neumann and Dirichlet boundary conditions. In order to do that, first, we put forward the concepts of negative continuation, exponential dichotomy and Dynamical Spectrum for linear skew product semiflows. Second, we set the problem in the skew product semiflow frame work and compute explicitly the dynamical spectrum for this semiflow. Finally, we compute the dynamical spectrum for a time dependent system of ordinary differential equations that is obtained by spatially discretizing of the parabolic equation
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