Global sharp gradient estimates for a nonlinear parabolic equation on Riemannian manifolds

In this paper, we employ the techniques in [C. Cavaterra, S. Dipierro, Z. Gao and E. Valdinoci, Global gradient estimates for a general type of nonlinear parabolic equations, J. Geom. Anal. 32 (2022), no. 2, Paper No. 65] and the approach in [H. T. Dung and N. T. Dung, Sharp gradient estimates for a heat equation in Riemannian manifolds, Proc. Amer. Math. Soc. 147 (2019), no. 12, 5329-5338] to derive sharp gradient estimates for a positive solution to the heat equation u(t) = Delta u + au log uin a complete noncompact Riemannian manifold (where a is a real constant). This is an extension of the gradient estimates of Dung and Dung.