Affiliation:
1. Faculty of Mathematics, Mechanics and Informatics , VNU – University of Science , Hanoi , Vietnam
Abstract
Abstract
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, 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, 12, 5329–5338]
to derive sharp gradient estimates for a positive solution to the heat equation
u
t
=
Δ
u
+
a
u
log
u
u_{t}=\Delta u+au\log u
in a complete noncompact Riemannian manifold (where a is a real constant). This is an extension of the gradient estimates of Dung and Dung.
Funder
VNU Science and Technology Development Fund
Subject
Applied Mathematics,Numerical Analysis,Analysis