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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
10.2. Poisson Equation
3
w + Φ(x) = 0 869
First boundary value problem.
The solution of the first boundary value problem for the Poisson equation
3
w + Φ(r) = 0 (1)
in a domain V with the nonhomogeneous boundary condition
w = f (r) for r S
can be represented in the form
w(r) =
Z
V
Φ(ρ)G(r, ρ) dV
ρ
Z
S
f(ρ)
∂G
∂N
ρ
dS
ρ
. (2)
Here, G(r, ρ) is the Green’s function of the first boundary value problem,
∂G
∂N
ρ
is the deriva-
tive of the Green’s function with respect to ξ, η, ζ along the outward normal N to the bound-
ary S of the domain V . The integration is everywhere with respect to ξ, η, ζ.
The volume elements in solution (2) for basic coordinate systems are presented ...
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Publisher Resources

ISBN: 9781466581494