@Article{JPDE-17-255,
author = {Boqing Dong },
title = {Asymptotic Behavior of the Nonlinear Parabolic Equations},
journal = {Journal of Partial Differential Equations},
year = {2004},
volume = {17},
number = {3},
pages = {255--263},
abstract = {<p>This paper is concerned with the large time behavior for solutions of the nonlinear parabolic equations in whole spaces R^n. The spectral decomposition methods of Laplace operator are applied and it is proved that if the initial data u_0 ∈ L² ∩ L^r for 1 ≤ r ≤ 2, then the solutions decay in L² norm at t^{-\frac{n}{2}(\frac{1}{r}-\frac{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.</p>},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5391.html}
}