scholarly journals Gradient Estimates for a Nonlinear Diffusion Equation on Complete Manifolds

2010 ◽  
Vol 23 (1) ◽  
pp. 68-79 ◽  
Author(s):  
Wu Jiayong
Keyword(s):  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
Gradient Estimates ◽  
Complete Manifolds

scholarly journals Gradient estimates for an orthotropic nonlinear diffusion equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Pierre Bousquet ◽  
Lorenzo Brasco ◽  
Chiara Leone ◽  
Anna Verde
Keyword(s):  
Parabolic Equation ◽  
Diffusion Equation ◽  
Weak Solutions ◽  
Nonlinear Diffusion ◽  
Degenerate Parabolic Equation ◽  
Nonlinear Diffusion Equation ◽  
Gradient Estimates ◽  
Lipschitz Continuous ◽  
Locally Lipschitz ◽  
Degenerate Parabolic

Abstract We consider a quasilinear degenerate parabolic equation driven by the orthotropic p-Laplacian. We prove that local weak solutions are locally Lipschitz continuous in the spatial variable, uniformly in time.

NONLINEAR DIFFUSION EQUATION WITH A PERTURBED CONVECTIONTERM: POTENTIAL SYMMETRIES WITH RESPECT TO THE SECOND CONSERVATION LAW

2021 ◽  
Vol 10 (5) ◽  
pp. 2611-2624
Author(s):  
O.K. Narain ◽  
F.M. Mahomed
Keyword(s):  
Diffusion Equation ◽  
Conservation Law ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
The Other ◽  
Linear Case ◽  
Exact Equation ◽  
Convection Term ◽  
Potential Symmetries ◽  
Perturbed Equation

We consider the nonlinear diffusion equation with a perturbed convection term. The potential symmetries for the exact equation with respect to the second conservation law are classified. It is found that these exist only in the linear case. It is further shown that no nontrivial approximate potential symmetries of order one exists for the perturbed equation with respect to the other conservation law.

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