Li-Yau estimates for a semilinear parabolic equation on an evolving manifold

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Abimbola Abolarinwa

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 aC2(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.

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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
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