Gradient estimates and liouville theorems for linear and nonlinear parabolic equations on riemannian manifolds

2016 ◽  
Vol 36 (2) ◽  
pp. 514-526 ◽  
Author(s):  
Xiaobao ZHU
Keyword(s):  
Riemannian Manifolds ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Gradient Estimates ◽  
Liouville Theorems ◽  
Nonlinear Parabolic ◽  
Linear And Nonlinear

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>

Prescribed conditions at infinity for parabolic equations

2014 ◽  
Vol 17 (01) ◽  
pp. 1450004 ◽  
Author(s):  
Shoshana Kamin ◽  
Fabio Punzo
Keyword(s):  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Parabolic Equations ◽  
Time Dependent ◽  
Bounded Solutions ◽  
Nonlinear Parabolic ◽  
Linear And Nonlinear ◽  
Conditions At Infinity

We are concerned with existence and uniqueness of the solutions for linear and nonlinear parabolic equations with time-dependent coefficients, in the class of bounded solutions satisfying appropriate conditions at infinity.

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