scholarly journals A nonlinear partial differential equation for the volume preserving mean curvature flow

2013 ◽  
Vol 8 (1) ◽  
pp. 9-22
Author(s):  
Dimitra Antonopoulou ◽  
◽  
Georgia Karali
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Nonlinear Partial Differential Equation ◽  
Curvature Flow ◽  
Partial Differential ◽  
Volume Preserving

scholarly journals A stochastic representation for the solution of approximated mean curvature flow

2022 ◽  
Vol 29 (1) ◽  
Author(s):  
Raffaele Grande
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Stochastic Representation ◽  
Partial Differential ◽  
Viscosity Sense ◽  
Appl Math

AbstractThe evolution by horizontal mean curvature flow (HMCF) is a partial differential equation in a sub-Riemannian setting with applications in IT and neurogeometry [see Citti et al. (SIAM J Imag Sci 9(1):212–237, 2016)]. Unfortunately this equation is difficult to study, since the horizontal normal is not always well defined. To overcome this problem the Riemannian approximation was introduced. In this article we obtain a stochastic representation of the solution of the approximated Riemannian mean curvature using the Riemannian approximation and we will prove that it is a solution in the viscosity sense of the approximated mean curvature flow, generalizing the result of Dirr et al. (Commun Pure Appl Math 9(2):307–326, 2010).

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

The Effective Dynamics of the Volume Preserving Mean Curvature Flow

2018 ◽  
Vol 172 (2) ◽  
pp. 458-476
Author(s):  
Ilias Chenn ◽  
G. Fournodavlos ◽  
I. M. Sigal
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Effective Dynamics ◽  
Volume Preserving
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