scholarly journals Axially-symmetric boundary-value problems

1965 ◽  
Vol 71 (6) ◽  
pp. 787-809 ◽  
Author(s):  
Albert E. Heins
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Axially Symmetric

scholarly journals An axially symmetric forced convection problem

1975 ◽  
Vol 20 (1) ◽  
pp. 1-17
Author(s):  
J. A. Belward
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Convection Heat Transfer ◽  
Fundamental Solutions ◽  
Integral Representations ◽  
Original Equation ◽  
Transfer Model ◽  
Axially Symmetric ◽  
Simple Diffusion ◽  
Diffusion Convection

AbstractA simple diffusion-convection heat transfer model is formulated which leads to an axially symmetric partial differential equation. The equation is shown to be closely related to a second one which is adjoint to the original equation in one variable can and be interpreted as a description of another diffusion-convection model. Fundamental solutions of the original equation are constructed and interpreted with reference to both models. Some boundary value problems are solved in series form and integral representations of the solutions are also given. The boundary value problems are shown to be equivalent to an integral equation and the correspondence between the two formulations is understood in terms of the two diffusion-convection problems. A Péclet number is defined in one of the boundary value problems and the behaviour of the solutions is studied for large and small values of this parameter.

scholarly journals Solution Behavior in the Vicinity of Characteristic Envelopes for the Double Slip and Rotation Model

2020 ◽  
Vol 10 (9) ◽  
pp. 3220 ◽  
Author(s):  
Yao Wang ◽  
Sergei Alexandrov ◽  
Elena Lyamina
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Strain Rate Tensor ◽  
Axially Symmetric ◽  
Natural Boundary ◽  
Rigid Plastic ◽  
Solution Behavior ◽  
Normal Distance ◽  
Approach Infinity ◽  
Rotation Model

The boundary conditions significantly affect solution behavior near rough interfaces. This paper presents general asymptotic analysis of solutions for the rigid plastic double slip and rotation model in the vicinity of an envelope of characteristics under plane strain and axially symmetric conditions. This model is used in the mechanics of granular materials. The analysis has important implications for solving boundary value problems because the envelope of characteristics is a natural boundary of the analytic solution. Moreover, an envelope of characteristics often coincides with frictional interfaces. In this case, the regime of sticking is not possible independently of the friction law chosen. It is shown that the solution is singular in the vicinity of envelopes. In particular, the profile of the velocity component tangential to the envelope is described by the sum of the constant and square root functions of the normal distance to the envelope in its vicinity. As a result, some components of the strain rate tensor approach infinity. This finding might help to develop an efficient numerical method for solving boundary value problems and provide the basis for the interpretation of some experimental results.

scholarly journals Boundary value problems of singular elliptic partial differential equations

1972 ◽  
Vol 13 (2) ◽  
pp. 111-118 ◽  
Author(s):  
Chi Yeung Lo
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Smooth Boundary ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Axially Symmetric ◽  
Dirichlet Problems ◽  
The Neumann Problem ◽  
Image Position ◽  
Generalized Axially Symmetric Potentials

In a recent paper [6], this author has extended the method of the kernel function [1] to the boundary value problems of the generalized axially symmetric potentialsThis method can also be applied to a more general class of singular differential equations, namelyor, equivalently,We shall derive in the sequel explicit formulas for the Dirichlet problems of (1.1) in the first quadrant of the x-y plane in terms of sufficiently smooth boundary data, and obtain an error-bound for their approximate solutions. We shall also indicate how the Neumann problem can be solved.

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