Li-Yau estimates for a semilinear parabolic equation on an evolving manifold
Main Article Content
Abstract
Let (M,g(t)) be a complete Riemannian manifold of dimension n, we obtain Li-Yau type gradient estimates on positive bounded solutions to the following semilinear parabolic equation
∂u(t,x) ∕ ∂t = Δ u(t,x) + a(x) us(t,x) -λu(t,x),
where (t,x) ∈ ([0,T] × M), T < ∞, s > 1, λ ∈ ℝ and a ∈ C2(M) on evolving Riemannian metrics g(t) with bounded below Ricci tensor. The application of our gradient estimates yields the classical differential Harnack inequality, which compares a solution at some time with those at previous time.
Downloads
Download data is not yet available.
Article Details
How to Cite
Abolarinwa, A. (2018). Li-Yau estimates for a semilinear parabolic equation on an evolving manifold. Gulf Journal of Mathematics, 6(1). https://doi.org/10.56947/gjom.v6i1.126
Issue
Section
Articles