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New Differential Harnack Inequalities for Nonlinear Heat Equations |
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Citation: |
Jiayong WU.New Differential Harnack Inequalities for Nonlinear Heat Equations[J].Chinese Annals of Mathematics B,2020,41(2):267~284 |
Page view: 720
Net amount: 558 |
Authors: |
Jiayong WU; |
Foundation: |
This work was supported by the National Natural Science
Foundation of China (No.11671141) and the Natural Science
Foundation of Shanghai (No.17ZR1412800). |
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Abstract: |
This paper deals with constrained trace, matrix and constrained
matrix Harnack inequalities for the nonlinear heat equation
$\omega_t=\Delta\omega+a\omega\ln \omega$ on closed manifolds. A new
interpolated Harnack inequality for
$\omega_t=\Delta\omega-\omega\ln\omega+\varepsilon R\omega$ on
closed surfaces under $\varepsilon$-Ricci f\/low is also derived.
Finally, the author proves a new differential Harnack inequality for
$\omega_t=\Delta\omega-\omega\ln\omega$ under Ricci f\/low without
any curvature condition. Among these Harnack inequalities, the
correction terms are all time-exponential functions, which are
superior to time-polynomial functions. |
Keywords: |
Harnack inequality, Nonlinear heat equation, Ricci f/low |
Classification: |
53C44 |
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