Abstract: The mild solution of a nonlinearnonautonomous evolutionary equation can be formulated as a skew product
semiflow in a product phase space. Under a spectral gap condition, it is shown
that there exists an inertial manifold for this skew product semiflow. Instead
of the Lyapunov-Perron method, the proof is fulfilled via the approach of conic
invariance and incrementally exponential dichotomy and based on two conic
differential inequalities. The construction of inertial manifold is made through
an exponentially tracking integral manifold, in which the pullback is achieved
also by the incremental dichotomy and a homotopy lemma. An illustration of the
applications is shown by nonautonomous reaction-diffusion equations.
Keywords and phrases: global dynamics, inertial manifold, integral manifold, nonautonomous evolutionary equation, skew product semiflow.
