Modified Boundary Value Problems For a Quasi-Linear Elliptic Equation

1956 ◽  
Vol 8 ◽  
pp. 203-219 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Continuous Function ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Elliptic Partial Differential Equation ◽  
Linear Elliptic Equation ◽  
Partial Differential

1. Introduction. The quasi-linear elliptic partial differential equation to be studied here has the form(1.1) Δu = − F(P,u).Here Δ is the Laplacian while F(P,u) is a continuous function of a point P and the dependent variable u. We shall study the Dirichlet problem for (1.1) and will find that the usual formulation must be modified by the inclusion of a parameter in the data or the differential equation, together with a further numerical condition on the solution.

scholarly journals Comparison results for nonlinear divergence structure elliptic PDE’s

2019 ◽  
Vol 9 (1) ◽  
pp. 438-448 ◽  
Author(s):  
Yichen Liu ◽  
Monica Marras ◽  
Giovanni Porru
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Elliptic Partial Differential Equation ◽  
Comparison Result ◽  
Partial Differential ◽  
Laplace Equations ◽  
Comparison Results ◽  
Divergence Structure

Abstract First we prove a comparison result for a nonlinear divergence structure elliptic partial differential equation. Next we find an estimate of the solution of a boundary value problem in a domain Ω in terms of the solution of a related symmetric boundary value problem in a ball B having the same measure as Ω. For p-Laplace equations, the corresponding result is due to Giorgio Talenti. In a special (radial) case we also prove a reverse comparison result.

Effective Approximation for Elliptic Partial Differential Equation with Periodical Boundary Value Problem

2010 ◽  
Vol 29-32 ◽  
pp. 1294-1300
Author(s):  
Xin Cai
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Elliptic Partial Differential Equation ◽  
Partial Differential ◽  
Layer Function ◽  
Smooth Component ◽  
Boundary Layer Function

Elliptic partial differential equation with periodical boundary value problem was considered. The equation would degenerate to parabolic partial differential equation when small parameter tends to zero. This is a multi-scale problem. Firstly, the property of boundary layer was discussed. Secondly, the boundary layer function was presented. The smooth component was constructed according to the boundary layer function. Thirdly, finite difference scheme for the smooth component is proposed according to transition point in time direction. Finally, experiment was proposed to illustrate that our presented method is an effective computational method.

scholarly journals On an integral transform

1979 ◽  
Vol 20 (1) ◽  
pp. 1-14 ◽  
Author(s):  
D. Naylor
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Integral Transform ◽  
Boundary Value ◽  
Partial Differential ◽  
Image Position

In this paper the author continues the search for a suitable integral transform that can be applied to certain boundary value problems involving the Helmholtz equation and the condition of radiation. The transform in question must be capable of eliminating the r-dependence appearing in the partial differential equation

The Three-Dimensional Hollow or Solid Truncated Cone Under Axisymmetric Torsionless End Loading

1976 ◽  
Vol 43 (1) ◽  
pp. 59-63 ◽  
Author(s):  
J. L. Klemm ◽  
R. Fernandes
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Total Stress ◽  
Partial Differential ◽  
Truncated Cone ◽  
Sample Application

The Saint-Venant problems of solid or hollow truncated cone are investigated under axisymmetric torsionless end loading with the ruled sides being free from stress. Total-stress problems are formulated in terms of a vector partial differential equation whose component variables are stresses or of stress-type. A biorthogonality condition is derived which permits the numerical solution of boundary-value problems, and the results of a sample application of the method are presented.

The Application of MATLAB in Classical Electrostatics Boundary-Value Problems

2013 ◽  
Vol 378 ◽  
pp. 602-608
Author(s):  
Fu Jian Zong ◽  
Jin Ma
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problems ◽  
Potential Function ◽  
Laplace Equation ◽  
Electrostatic Field ◽  
Computer Image ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Partial Differential

In this paper we introduce the use of a computer image and the Partial Differential Equation (PDE) Toolbox in MATLAB, and discuss the electrostatic field, the potential function and the solution of the Laplace equation by separation of variables and the PDE toolbox. It is convenient to figure out the classical electrostatics problem with MATLAB.

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