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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
648 SECOND-ORDER HYPERBOLIC EQUATIONS WITH TWO SPACE VARIABLES
Here, the µ
n
and β
m
are positive roots of the transcendental equations
µJ
1
(µ) k
1
RJ
0
(µ) = 0,
tan(βl)
β
=
k
2
+ k
3
β
2
k
2
k
3
.
Domain: 0 r R, 0 z l. Mixed boundary value problems.
1
. A circular cylinder of finite length is considered. The following conditions are pre-
scribed:
w = f
0
(r, z) at t = 0 (initial condition),
t
w = f
1
(r, z) at t = 0 (initial condition),
w = g
1
(z, t) at r = R (boundary condition),
z
w = g
2
(r, t) at z = 0 (boundary condition),
z
w = g
3
(r, t) at z = l (boundary condition).
Solution:
w(r, z, t)=
∂t
Z
l
0
Z
R
0
f
0
(ξ, η)G(r, z, ξ, η, t) +
Z
l
0
Z
R
0
f
1
(ξ, η)G(r, z, ξ, η, t) dη ...
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Publisher Resources

ISBN: 9781466581494