A Sixth Order Curvature Flow of Plane Curves with Boundary Conditions

2019 ◽  
pp. 213-221
Author(s):  
James McCoy ◽  
Glen Wheeler ◽  
Yuhan Wu
Keyword(s):  
Boundary Conditions ◽  
Curvature Flow ◽  
Sixth Order ◽  
Plane Curves

scholarly journals A sixth order flow of plane curves with boundary conditions

2020 ◽  
Vol 72 (3) ◽  
pp. 379-393
Author(s):  
James McCoy ◽  
Glen Wheeler ◽  
Yuhan Wu
Keyword(s):  
Boundary Conditions ◽  
Sixth Order ◽  
Plane Curves ◽  
Order Flow

On an area-preserving inverse curvature flow of convex closed plane curves

2021 ◽  
Vol 280 (8) ◽  
pp. 108931
Author(s):  
Laiyuan Gao ◽  
Shengliang Pan ◽  
Dong-Ho Tsai
Keyword(s):  
Curvature Flow ◽  
Plane Curves ◽  
Area Preserving ◽  
Closed Plane

Gradient Estimates for Spacelike Mean Curvature Flow with Boundary Conditions

2018 ◽  
Vol 62 (2) ◽  
pp. 459-469
Author(s):  
Ben Lambert
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Mean Curvature ◽  
Neumann Boundary Condition ◽  
Mean Curvature Flow ◽  
Neumann Boundary ◽  
Curvature Flow ◽  
Gradient Estimate ◽  
Gradient Estimates ◽  
The Mean

AbstractWe prove a gradient estimate for graphical spacelike mean curvature flow with a general Neumann boundary condition in dimension n = 2. This then implies that the mean curvature flow exists for all time and converges to a translating solution.

scholarly journals Global Attractors of Sixth Order PDEs Describing the Faceting of Growing Surfaces

2015 ◽  
Vol 28 (1) ◽  
pp. 49-67 ◽  
Author(s):  
M. D. Korzec ◽  
P. Nayar ◽  
P. Rybka
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Initial Conditions ◽  
Periodic Boundary Conditions ◽  
Global Attractors ◽  
Sixth Order ◽  
Two Dimensional ◽  
One Dimensional ◽  
Crystalline Surface ◽  
Dimensional Version

Abstract A spatially two-dimensional sixth order PDE describing the evolution of a growing crystalline surface h(x, y, t) that undergoes faceting is considered with periodic boundary conditions, as well as its reduced one-dimensional version. These equations are expressed in terms of the slopes $$u_1=h_{x}$$ u 1 = h x and $$u_2=h_y$$ u 2 = h y to establish the existence of global, connected attractors for both equations. Since unique solutions are guaranteed for initial conditions in $$\dot{H}^2_{per}$$ H ˙ p e r 2 , we consider the solution operator $$S(t): \dot{H}^2_{per} \rightarrow \dot{H}^2_{per}$$ S ( t ) : H ˙ p e r 2 → H ˙ p e r 2 , to gain our results. We prove the necessary continuity, dissipation and compactness properties.

scholarly journals Multiple Solutions for a Sixth Order Boundary Value Problem

2021 ◽  
Vol 22 (1) ◽  
pp. 1-12
Author(s):  
A. L. M. Martinez ◽  
C. A. Pendeza Martinez ◽  
G. M. Bressan ◽  
R. M. Souza ◽  
E. W. Stiegelmeier
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Order Equation ◽  
Sixth Order ◽  
Contraction Principle ◽  
Banach’S Contraction Principle

This work presents conditions for the existence of multiple solutions for a sixth order equation with homogeneous boundary conditions using Avery Peterson's theorem. In addition, non-trivial examples are presented and a new numerical method based on the Banach's Contraction Principle is introduced.  

scholarly journals Parametric quintic spline solution for sixth order two point boundary value problems

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1233-1245 ◽  
Author(s):  
Arshad Khan ◽  
Talat Sultana
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sixth Order ◽  
Point Boundary ◽  
Spline Method ◽  
Quintic Spline ◽  
Practical Usefulness ◽  
Special Case ◽  
Boundary Equations

In this paper, parametric quintic spline method is presented to solve a linear special case sixth order two point boundary value problems with two different cases of boundary conditions. The method presented in this paper has been shown to be second and fourth order accurate. Boundary equations are derived for both the cases of boundary conditions. Convergence analysis of these methods are discussed. The presented method is tested on four numerical examples of linear sixth order boundary value problems. Comparison is made to show the practical usefulness of the presented method.

Numerical Assessment of the Boundary Layer Effect Predicted by the Shear Flexible Beam Theory with the Sixth-Order Differential Equations

2011 ◽  
Vol 105-107 ◽  
pp. 1705-1711
Author(s):  
Xiao Dan Wang ◽  
Guang Yu Shi
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Beam Theory ◽  
Sixth Order ◽  
Flexible Beam ◽  
Element Analysis ◽  
Flexible Beams ◽  
Displacement Boundary ◽  
Numerical Assessment ◽  
Layer Effect

The analytical solutions of shear flexible beams with displacement boundary conditions are derived by using the new sixth-order differential equation beam theory presented by Shi and Voyiadjis (ASME J. Appl. Mech., Vol. 78, 021019, 2011), in which the boundary layer effects are included. The accuracy of the boundary layer effects predicted by the new sixth-order beam theory is evaluated by the finite element analysis in this study. The numerical results show that the new sixth-order beam theory is capable of taking account of the displacement boundary conditions of shear deformable beams and predicting good results of the boundary layer effects induced by the displacement boundaries and the continuity constraints.

Compatibility Equations in the Theory of Elasticity

2003 ◽  
Vol 125 (2) ◽  
pp. 244-245 ◽  
Author(s):  
Igor V. Andrianov ◽  
Jan Awrejcewicz
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Sixth Order ◽  
Operational Method ◽  
Equilibrium Equations ◽  
Additional Boundary Conditions

It is shown by operational method that the boundary value problem of the theory of elasticity related to stresses, which can be reduced to three strains compatibility equations and to three equilibrium equations, in fact is of sixth order. Hence, it is not required to formulate additional boundary conditions.

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