New Differential Harnack Inequalities for Nonlinear Heat Equations Citation： Jiayong WU.New Differential Harnack Inequalities for Nonlinear Heat Equations[J].Chinese Annals of Mathematics B,2020,41(2):267~284 Page view： 40        Net amount： 50 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). 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 Download PDF Full-Text