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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
17.5. Construction of the Green’s Functions. General Formulas and Relations 1229
3
. Third boundary value problem. The boundary condition:
z
w kw = f(x) at z = 0.
Green’s function:
G(x, y, z, ζ) = E
e
(x, y, z ζ) + E
e
(x, y, z + ζ) 2k
Z
0
e
ks
E
e
(x, y , z + ζ + s) ds
= E
e
(x, y, z ζ) + E
e
(x, y, z + ζ) 2k
Z
z+ζ
e
k(σzζ)
E
e
(x, y , σ) dσ.
Domain: x R
n
, 0 z l. Problems for elliptic equations.
1
. First boundary value problem. Boundary conditions:
w = f
1
(x) at z = 0, w = f
2
(x) at z = l.
Green’s function:
G(x, y, z, ζ) =
X
n=−∞
E
e
(x, y, z ζ + 2nl) E
e
(x, y, z + ζ + 2nl)
. (17.5.3.3)
Domain of the free parameters: y R
n
and 0 ζ l.
2
. Second boundary ...
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Publisher Resources

ISBN: 9781466581494