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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
730 SECOND-ORDER HYPERBOLIC EQUATIONS WITH THREE OR MORE SPA CE VARIABLES
Here,
G(r, ϕ, z, ξ, η, ζ, t) =
1
πR
2
l
X
n=0
X
m=1
X
k=0
A
n
A
k
[J
n
(µ
nm
R)]
2
λ
nmk
J
n
(µ
nm
r)J
n
(µ
nm
ξ)
× cos[n(ϕ η)] cos
kπz
l
cos
kπζ
l
sin
t
p
λ
nmk
,
λ
nmk
= a
2
µ
2
nm
+
a
2
k
2
π
2
l
2
+ b, A
n
=
(
1 for n = 0,
2 for n > 0,
where the J
n
(ξ) are Bessel functions (the prime denotes a derivative with respect to the
argument) and the µ
nm
are positive roots of the transcendental equation J
n
(µR) = 0.
2
. A circular cylinder of finite length is considered. The following conditions are pre-
scribed:
w = f
0
(r, ϕ, z) at t = 0 (initial condition),
t
w = f
1
(r, ϕ, z) at t = 0 (initial condition),
r
w = g
1
(ϕ, z, t) at r = R (boundary ...
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Publisher Resources

ISBN: 9781466581494