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Let ( M n  ,  F ( t ),  m ),  t  ∈ [0,  T ], be a compact Finsler manifold with  F ( t ) evolving by the Finsler-geometric flow∂  g  (  x  ,  t  )    ∂  t    =  2  h  (  x  ,  t  )  ,$\begin{array}{} \displaystyle \frac{\partial g(x,t)}{\partial t}=2h(x,t), \end{array}$    where  g ( t ) is the symmetric metric tensor associated with  F , and  h ( t ) is a symmetric (0, 2)-tensor. In this paper, we consider local Li-Yau type gradient estimates for positive solutions of the following nonlinear heat equation with potential

The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow