A numerical solution for the laplace equation with normal derivative boundary condition

The boundary value problem for the Laplace equation outside several cracks in a plane is studied. The jump of the solution of the Laplace equation and the boundary condition containing the jump of its normal derivative are specified on the cracks. The problem has unique classical solution under certain conditions. The new integral representation for the unique solution of this problem is obtained. The problem is reduced to the uniquely solvable Fredholm equation of the second kind and index zero. The integral representation and integral equation are essentially simpler than those derived for this problem earlier. The singularities at the ends of the cracks are investigated.

Download Full-text

On the use of an integral equation approach for the numerical solution of a Cauchy problem for Laplace equation in a doubly connected planar domain

Inverse Problems in Science and Engineering ◽

10.1080/17415977.2013.829467 ◽

2013 ◽

Vol 22 (1) ◽

pp. 130-149 ◽

Cited By ~ 9

Author(s):

Roman Chapko ◽

B. Tomas Johansson ◽

Yuriy Savka

Keyword(s):

Integral Equation ◽

Cauchy Problem ◽

Numerical Solution ◽

Laplace Equation ◽

Planar Domain ◽

Equation Approach ◽

Integral Equation Approach

Download Full-text

The Third Problem for the Laplace Equation with a Boundary Condition from Lp

Integral Equations and Operator Theory ◽

10.1007/s00020-003-1354-5 ◽

2005 ◽

Vol 54 (2) ◽

pp. 235-258 ◽

Cited By ~ 3

Author(s):

Dagmar Medková

Keyword(s):

Boundary Condition ◽

Laplace Equation ◽

The Third

Download Full-text

Numerical solution of nonlinear inverse heat conduction problem with a radiation boundary condition

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.1620200608 ◽

1984 ◽

Vol 20 (6) ◽

pp. 1057-1066 ◽

Cited By ~ 13

Author(s):

R. C. Mehta

Keyword(s):

Boundary Condition ◽

Heat Conduction ◽

Numerical Solution ◽

Heat Conduction Problem ◽

Inverse Heat Conduction Problem ◽

Inverse Heat Conduction ◽

Radiation Boundary Condition ◽

Radiation Boundary

Download Full-text

On the Laplace equation with a supercritical nonlinear Robin boundary condition in the half-space

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-012-0531-2 ◽

2012 ◽

Vol 47 (3-4) ◽

pp. 667-682 ◽

Cited By ~ 1

Author(s):

Lucas C. F. Ferreira ◽

Everaldo S. Medeiros ◽

Marcelo Montenegro

Keyword(s):

Boundary Condition ◽

Half Space ◽

Laplace Equation ◽

Robin Boundary Condition ◽

Robin Boundary

Download Full-text

Degenerate scale for 2D Laplace equation with mixed boundary condition and comparison with other conditions on the boundary

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2017.12.004 ◽

2018 ◽

Vol 88 ◽

pp. 14-25 ◽

Cited By ~ 2

Author(s):

A. Corfdir ◽

G. Bonnet

Keyword(s):

Boundary Condition ◽

Laplace Equation ◽

Mixed Boundary Condition ◽

Mixed Boundary ◽

Degenerate Scale

Download Full-text

Explicit solution of the jump problem for the Laplace equation and singularities at the edges

Mathematical Problems in Engineering ◽

10.1155/s1024123x01001491 ◽

2001 ◽

Vol 7 (1) ◽

pp. 1-13 ◽

Cited By ~ 9

Author(s):

P. A. Krutitskii

Keyword(s):

Boundary Value Problem ◽

Explicit Form ◽

Laplace Equation ◽

Explicit Solution ◽

Existence Theorems ◽

Single Layer ◽

Normal Derivative ◽

Jump Problem ◽

Uniqueness And Existence ◽

Conditions At Infinity

The boundary value problem for the Laplace equation outside several cuts in a plane is studied. The jump of the solution of the Laplace equation and the jump of its normal derivative are specified on the cuts. The problem is studied under different conditions at infinity, which lead to different uniqueness and existence theorems. The solution of this problem is constructed in the explicit form by means of single layer and angular potentials. The singularities at the ends of the cuts are investigated.

Download Full-text