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For nonlinear parabolic evolution equations, it is proved that, under the assumptions of localLipschitz continuity of nonlinearity and the dissipativity of semiflows, there exist approximate inertialmanifolds (AIM) in the energy space and that the approximate inertial manifolds are constructed as thegraph of the steady-state determining mapping based on the spectral decomposition. It is also shown thatthe thickness of the exponentially attracting neighborhood of the AIM converges to zero at a fractionalpower rate as the dimension of the AIM increases. Applications of the obtained results to Burgers'equation, higher dimensional reaction-diffusion equations, 2D Ginzburg-Landau equations, and axiallysymmetric Kuramoto-Sivashinsky equations in annular domains are included

Approximate inertial manifolds for nonlinear parabolic equations via steady-state determining mapping