GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LINEAR AND NONLINEAR PARABOLIC EQUATIONS ON RIEMANNIAN

• 作 者: 朱晓宝
• 机 构: DepartmentofMathematics
• 出 处: 数学物理学报：B辑英文版
• 发表日期: 2016年2期
• 关键词: Gradient estimate linear parabolic equation nonlinear parabolic equation Liouvil
• 基金项目: This work is partially supported by the National Science Foundation of China （41275063 and 11401575）.

In this article, we will derive local elliptic type gradient estimates for positive solutions of linear parabolic equations(?-?/(?t))u(x, t) + h(x,t)u(x,t) = 0 and nonlinear parabolic equations(?-?-/(?t))u(x,t) + h(x, t)u~p(x,t) = 0(p > 1) on Riemannia