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   

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