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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
796 SECOND-ORDER ELLIPTIC EQUATIONS WITH TWO SPACE VARIABLES
Third boundary value problem.
The solution of the third boundary value problem for the Poisson equation (1) in the do-
main S with the nonhomogeneous boundary condition
∂w
∂N
+ kw = f(r) for r L
is given by formula (5) with C = 0, where G = G(r, ρ) is the Green’s function of the third
boundary value problem and is determined by the following conditions:
1
. The function G satisfies the Laplace equation in x, y in the domain S everywhere
except for the point (ξ, η), at which G has a singularity of the form
1
2π
ln
1
|rρ|
.
2
. With respect to x, y, the function G satisfies the homogeneous bound
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Publisher Resources

ISBN: 9781466581494