scholarly journals Pointwise gradient estimates of solutions to onedimensional nonlinear parabolic equations

2003 ◽  
Vol 3 (4) ◽  
pp. 577-602 ◽  
Author(s):  
Philippe Bénilan † ◽  
Jesús Ildefonso Díaz
Keyword(s):  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Gradient Estimates ◽  
Estimates Of Solutions ◽  
Nonlinear Parabolic

scholarly journals Hamilton-Souplet-Zhang’s Gradient Estimates for Two Types of Nonlinear Parabolic Equations under the Ricci Flow

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Guangyue Huang ◽  
Bingqing Ma
Keyword(s):  
Ricci Flow ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
The Other ◽  
Gradient Estimates ◽  
Nonlinear Parabolic

We consider gradient estimates for two types of nonlinear parabolic equations under the Ricci flow: one is the equationut=Δu+aulog⁡u+buwitha,bbeing two real constants; the other isut=Δu+λuαwithλ,αbeing two real constants. By a suitable scaling for the above two equations, we obtain Hamilton-Souplet-Zhang-type gradient estimates.

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