scholarly journals A boundary-value problem for the biharmonic equation and the iterated Laplacian in a 3D-domain with an edge

2007 ◽  
Vol 143 (2) ◽  
pp. 2936-2960
Author(s):  
S. A. Nazarov ◽  
G. H. Sweers
Keyword(s):  
Boundary Value Problem ◽  
Biharmonic Equation ◽  
Boundary Value

scholarly journals Biharmonic Equation on Annulus in a Unit Sphere with Polynomial Boundary Condition

2017 ◽  
Vol 13 (1) ◽  
pp. 51
Author(s):  
Ikhsan Maulidi ◽  
Agah D Garnadi
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Unit Sphere ◽  
Biharmonic Equation ◽  
Boundary Value ◽  
Boundary Function ◽  
Exact Algorithms ◽  
Polynomial Functions ◽  
Dirichlet Conditions ◽  
Laplace Equations

We studied Biharmonic boundary value problem on annulus with polynomial data. We utilize an exact algorithms for solving Laplace equations with Dirichlet conditions with polynomial functions data. The algorithm requires differentiation of the boundary function, but no integration.

On a boundary value problem for the biharmonic equation

2015 ◽  
Author(s):  
Tynysbek Sh. Kal’menov ◽  
Ulzada A. Iskakova
Keyword(s):  
Boundary Value Problem ◽  
Biharmonic Equation ◽  
Boundary Value

THE METHOD OF FUNDAMENTAL SOLUTIONS FOR AN INVERSE INTERNAL BOUNDARY VALUE PROBLEM FOR THE BIHARMONIC EQUATION

2009 ◽  
Vol 06 (04) ◽  
pp. 557-567 ◽  
Author(s):  
D. LESNIC ◽  
A. ZEB
Keyword(s):  
Boundary Value Problem ◽  
Biharmonic Equation ◽  
Numerical Solutions ◽  
Least Squares Method ◽  
Regularization Parameter ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Internal Boundary ◽  
Unknown Boundary

In this paper, an inverse internal boundary value problem associated to the biharmonic equation is considered. The problem consists of determining unknown boundary conditions from extra interior measurements. The method of fundamental solutions (MFS) is used to discretize the problem and the resulting ill-conditioned system of linear equations is solved using the Tikhonov regularization technique. It is shown that, unlike the least-squares method, the MFS-regularization numerical technique produces stable and accurate numerical solutions for an appropriate choice of the regularization parameter given by the L-curve criterion.

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