非线性热方程解的大时间行为

摘要

考虑多维空间中非线性热方程解的大时间行为，利用先验估计并构造近似格林函数，获得了非线性热方程解关于平面扩散波的非线性稳定性，并得到了整体解关于时间的最优衰减率。%This paper deals with large time behavior of solutions to multi-dimensional nonlinear heat equation.Using the prior estimation and constructing an approximate Green function,we proved that the planar diffusion wave was nonlinearly stable for the nonlinear heat equation.Besides,the optimal time decay rates are established.