期刊论文详细信息
Electronic Journal of Differential Equations | 卷:2015 |
Gradient estimates for a nonlinear parabolic equation with potential under geometric flow | |
Abimbola Abolarinwa1  | |
[1] Univ. of Sussex, Brighton, UK ; | |
关键词: Gradient estimates; Harnack inequalities; parabolic equations; geometric flows; | |
DOI : | |
来源: DOAJ |
【 摘 要 】
Let (M,g) be an n dimensional complete Riemannian manifold. In this article we prove local Li-Yau type gradient estimates for all positive solutions to thenonlinear parabolic equation $$ (\partial_t - \Delta_g + \mathcal{R}) u( x, t) = - a u( x, t) \log u( x, t) $$ along the generalised geometric flow on M. Here $\mathcal{R} = \mathcal{R} (x, t)$ is a smooth potential function and a is an arbitrary constant. As an application we derive a global estimate and a space-time Harnack inequality.
【 授权许可】
Unknown