紧致黎曼流形上一类非线性热方程的梯度估计

Gradient Estimates for a Nonlinear Heat Equation on Compact Riemannian Manifold

中文关键词:  非线性热方程  黎曼流形  梯度估计.

英文关键词:nonlinear heat equation  Riemannian manifold  gradient estimates.

中文摘要:

      本文我们研究了定义在带边及不带边的紧致黎曼流形上一类非线性热方程$u_t-\triangle u=au\log u $ 的梯度估计.在闭流形上我们得到了这个方程的光滑正解的 Hamilton 型梯度估计,且在紧致带非凸边界的流形上我们得到了这个方程的光滑正解的 Li-Yau型梯度估计.

英文摘要:

      In this paper, we study gradient estimates for the nonlinear heat equation $u_t-\triangle u=au\log u$, on compact Riemannian manifold with or without boundary. We get a Hamilton type gradient estimate for the positive smooth solution to the equation on close manifold, and obtain a Li-Yau type gradient estimate for the positive smooth solution to the equation on compact manifold with nonconvex boundary.