Gradient estimates for a nonlinear parabolic equation on complete smooth metric measure spaces
In this paper, the authors study gradient estimates for positive smooth solutions to the nonlinear parabolic equation \[(\Delta_\phi-q-\partial_t)u=au(\ln u)^\alpha \] on a smooth metric measure space \((M, g, e^{-\phi} dv)\), where \(q(x, t)\) is a smooth space-time function and \(a,\alpha\) are real constants. Further, using these estimation, the corresponding Harnack inequality is derived.
scientific article; zbMATH DE number 7388028
scientific article