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arXiv · 1803.10622

New differential Harnack inequalities for nonlinear heat equations

Jia-Yong Wu
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Abstract

We prove constrained trace, matrix and constrained matrix Harnack inequalities for the nonlinear heat equation $\omega_t=\Delta\omega+a\omega\ln \omega$ on closed manifolds. We also derive a new interpolated Harnack inequality for the equation $\omega_t=\Delta\omega-\omega\ln\omega+\varepsilon R\omega$ on closed surfaces under the $\varepsilon$-Ricci flow. Finally we prove a new differential Harnack inequality for the equation $\omega_t=\Delta\omega-\omega\ln\omega$ under the Ricci flow without any curvature condition. Among these Harnack inequalities, the correction terms are all time-exponential functions, which are superior to time-polynomial functions.

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Jia-Yong Wu. 2018-03-28. New differential Harnack inequalities for nonlinear heat equations. https://arxiv.org/abs/1803.10622

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