Hamilton-Souplet-Zhang's gradient estimates for two types of nonlinear parabolic equations under the Ricci flow (Q5964434)

Summary: We consider gradient estimates for two types of nonlinear parabolic equations under the Ricci flow: one is the equation \(u_t = \Delta u + a u \log u + b u\) with \(a, b\) being two real constants; the other is \(u_t = \Delta u + \lambda u^\alpha\) with \(\lambda, \alpha\) being two real constants. By a suitable scaling for the above two equations, we obtain Hamilton-Souplet-Zhang-type gradient estimates.