R^2上一类非线性抛物方程弱解的渐近性态

ASYMPTOTIC BEHAVIOR OF THE NONLINEAR PARABOLIC EQUATION IN R^2

本文研究R2上一类非线性抛物方程弱解的渐近性态,利用改进的Fourier分解方法,证明了其解在L2范数下的衰减速率为(1+t)^(-1/2),与在相同初值条件下线性热方程解的衰减速率是一致的.

In this paper the authors study the time decay of the weak solution to the nonlinear parabolic equation in R^2 and prove that the weak solution decays in L^2 norm at （1＋t）^-1/2.The result is sharp in the sense that it coincides with that of the solution to the linear heat equation.