Coupled scalar potential formulations for three-dimensional E.M. boundary value problems in inhomogeneous isotropic axially-symmetric media

2005 ◽  
Author(s):  
S. Chang ◽  
M. Morgan ◽  
K. Mei
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Scalar Potential ◽  
Three Dimensional ◽  
Axially Symmetric

scholarly journals Mixed Boundary-Value Problems in Potential Theory

1979 ◽  
Vol 22 (2) ◽  
pp. 91-98 ◽  
Author(s):  
A. H. England
Keyword(s):  
Boundary Value Problems ◽  
Potential Theory ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Analytical Techniques ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Mixed Boundary Value Problems

The problems associated with finding solutions of Laplace's equation subject to mixed boundary conditions have attracted much attention and, as a consequence, a variety of analytical techniques have been developed for the solution of such problems. Sneddon (1) has given a comprehensive account of these techniques. The object of this note is to draw attention to some simple orthogonal polynomial solutions to the most basic mixed boundary-value problems in two and threedimensional potential theory. These solutions have the advantage that most quantities of physical interest are easily evaluated in terms of known functions. Two-dimensional problems are considered in §2 and axially-symmetric three-dimensional problems in §3.

scholarly journals Initial boundary value problems for the three-dimensional compressible elastic Navier-Stokes-Poisson equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1356-1383
Author(s):  
Yong Wang ◽  
Wenpei Wu
Keyword(s):  
Equilibrium State ◽  
Boundary Value Problems ◽  
Electrostatic Potential ◽  
Boundary Value ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Navier Stokes ◽  
Initial Boundary Value Problems ◽  
Poisson Equations ◽  
Initial Boundary Value

Abstract We study the initial-boundary value problems of the three-dimensional compressible elastic Navier-Stokes-Poisson equations under the Dirichlet or Neumann boundary condition for the electrostatic potential. The unique global solution near a constant equilibrium state in H 2 space is obtained. Moreover, we prove that the solution decays to the equilibrium state at an exponential rate as time tends to infinity. This is the first result for the three-dimensional elastic Navier-Stokes-Poisson equations under various boundary conditions for the electrostatic potential.

Basic Boundary Value Problems of Thermoelasticity for Anisotropic Bodies with Cuts. I

1995 ◽  
Vol 2 (2) ◽  
pp. 123-140
Author(s):  
R. Duduchava ◽  
D. Natroshvili ◽  
E. Shargorodsky
Keyword(s):  
Boundary Value Problems ◽  
Displacement Vector ◽  
Boundary Value ◽  
Three Dimensional ◽  
Manifolds With Boundary ◽  
Hölder Continuous ◽  
Arbitrary Configuration ◽  
Anisotropic Bodies ◽  
Potential Methods ◽  
Basic Boundary

Abstract The three-dimensional problems of the mathematical theory of thermoelasticity are considered for homogeneous anisotropic bodies with cuts. It is assumed that the two-dimensional surface of a cut is a smooth manifold of an arbitrary configuration with a smooth boundary. The existence and uniqueness theorems for boundary value problems of statics and pseudo-oscillations are proved in the Besov and Bessel-potential spaces by means of the classical potential methods and the theory of pseudodifferential equations on manifolds with boundary. Using the embedding theorems, it is proved that the solutions of the considered problems are Hölder continuous. It is shown that the displacement vector and the temperature distribution function are Cα -regular with any exponent α < 1/2. This paper consists of two parts. In this part all the principal results are formulated. The forthcoming second part will deal with the auxiliary results and proofs.

Solutions to Particular Three-Dimensional Boundary Value Problems of Elastostatics

2013 ◽  
pp. 209-218
Author(s):  
Reza Eslami ◽  
Richard B. Hetnarski ◽  
Jozef Ignaczak ◽  
Naotake Noda ◽  
Naobumi Sumi ◽  
...  
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Dimensional Boundary
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