This paper is concerned with the large time behavior for solutions of the nonlinear parabolic equations in whole spaces Rn. The spectral decomposition methods of Laplace operator are applied and it is proved that if the initial data uo ∈ L2 ∩ Lrfor 1(<-) r(<-)2, then the solutions decay in L2 norm at t-n/2(1/r-1/2) . The decay rates are optimal in the sense that they coincide with the decay rates of the solutions to the heat equations with the same initial data.
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