关键词: 非线性热方程, 格林函数, 平面扩散波, 衰减估计

Abstract:

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.

Key words: nonlinear heat equation, Green function, planar diffusion wave, decay estimate