scholarly journals Global Gradient Estimates for a General Type of Nonlinear Parabolic Equations

2022 ◽  
Vol 32 (2) ◽  
Author(s):  
Cecilia Cavaterra ◽  
Serena Dipierro ◽  
Zu Gao ◽  
Enrico Valdinoci
Keyword(s):  
Parabolic Equations ◽  
General Type ◽  
Nonlinear Parabolic Equations ◽  
Gradient Estimates ◽  
Nonlinear Parabolic

scholarly journals Hamilton type gradient estimates for a general type of nonlinear parabolic equations on Riemannian manifolds

2021 ◽  
Vol 6 (10) ◽  
pp. 10506-10522
Author(s):  
Fanqi Zeng ◽  
Keyword(s):  
Riemannian Manifolds ◽  
Parabolic Equations ◽  
General Type ◽  
Nonlinear Parabolic Equations ◽  
Complete Riemannian Manifold ◽  
Gradient Estimates ◽  
Geometric Flow ◽  
Liouville Type ◽  
Nonlinear Parabolic ◽  
Liouville Type Theorems

<abstract><p>In this paper, we prove Hamilton type gradient estimates for positive solutions to a general type of nonlinear parabolic equation concerning $ V $-Laplacian:</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ (\Delta_{V}-q(x, t)-\partial_{t})u(x, t) = A(u(x, t)) $\end{document} </tex-math></disp-formula></p> <p>on complete Riemannian manifold (with fixed metric). When $ V = 0 $ and the metric evolves under the geometric flow, we also derive some Hamilton type gradient estimates. Finally, as applications, we obtain some Liouville type theorems of some specific parabolic equations.</p></abstract>

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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