The Harnack estimate for a nonlinear parabolic equation under the Ricci flow

2011 ◽  
Vol 27 (10) ◽  
pp. 1935-1940 ◽  
Author(s):  
Song Bo Hou
Keyword(s):  
Parabolic Equation ◽  
Ricci Flow ◽  
Nonlinear Parabolic Equation ◽  
Harnack Estimate ◽  
Nonlinear Parabolic

scholarly journals Gradient Estimates for a Weighted Γ-nonlinear Parabolic Equation Coupled with a Super Perelman-Ricci Flow and Implications

2021 ◽  
Author(s):  
Ali Taheri
Keyword(s):  
Parabolic Equation ◽  
Ricci Flow ◽  
Nonlinear Parabolic Equation ◽  
Type Theorem ◽  
Gradient Estimates ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Harnack Inequalities ◽  
Nonlinear Parabolic ◽  
Special Cases

AbstractThis article studies a nonlinear parabolic equation on a complete weighted manifold where the metric and potential evolve under a super Perelman-Ricci flow. It derives elliptic gradient estimates of local and global types for the positive solutions and exploits some of their implications notably to a general Liouville type theorem, parabolic Harnack inequalities and classes of Hamilton type dimension-free gradient estimates. Some examples and special cases are discussed for illustration.

scholarly journals $L^{\infty }$ decay estimates of solutions of nonlinear parabolic equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hui Wang ◽  
Caisheng Chen
Keyword(s):  
Parabolic Equation ◽  
Weak Solutions ◽  
Nonlinear Parabolic Equation ◽  
Divergence Form ◽  
Decay Estimates ◽  
Laplacian Equation ◽  
Estimates Of Solutions ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear ◽  
Doubly Nonlinear Parabolic Equation

AbstractIn this paper, we are interested in $L^{\infty }$ L ∞ decay estimates of weak solutions for the doubly nonlinear parabolic equation and the degenerate evolution m-Laplacian equation not in the divergence form. By a modified Moser’s technique we obtain $L^{\infty }$ L ∞ decay estimates of weak solutiona.

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