TY - JOUR
T1 - Asymptotic Behavior of the Nonlinear Parabolic Equations
JO - Journal of Partial Differential Equations
VL - 3
SP - 255
EP - 263
PY - 2004
DA - 2004/08
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5391.html
KW - L² decay
KW - spectral decomposition
KW - nonlinear parabolic equation
AB - <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>