Differential Harnack Estimates for Time-Dependent Heat Equations with Potentials

By Xiaodong Cao, R. Hamilton. 2008

116 citations recorded by the source corpus.

In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positive solution of the time-dependent heat equation.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fbaede3fc6a9b4c35c83525b7ecc6035588b7ef6

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Gradient estimates for positive solutions of the heat equation under geometric flow (2011, unknown): “Since then, there have been many works on gradient estimates along the Ricci flow or the conjugate Ricci flow for the solution of the heat equation or the conjugate heat equation; examples include [Cao 2008; Cao and Hamilton 2009; Kuang and Zhang 2008; Zhang 2006].”
Differential Harnack estimates for a nonlinear heat equation (2013, background): “In [1,2], the first author used a new idea of undetermined coefficients to systematically search for new Harnack inequalities.”
The conjugate heat equation and Ancient solutions of the Ricci flow (2010, methodology): “Since uk is a dilation of G(x, τ ;x0, 0), we derive that uk(x0, s) ≥ 1 2a1 > 0 for s ∈ [1, 4].”
Gradient estimates for the heat equation under the Ricci flow (2009, methodology): “The method we use is rather traditional; see, for example, [27, Chapter IV] and [6].”
Space of Ricci Flows I (2009, background): “[123], [12]) and the fact dgi(0)(yi, xi) < C implies that | log wi(xi, 0)| is uniformly bounded.”