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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
446 SECOND-ORDER PARABOLIC EQUATIONS WITH TWO SPACE VARIABLES
Here,
G(r, z, ξ, η, t) = G
1
(r, ξ, t) G
2
(z, η, t),
G
1
(r, ξ, t) =
1
πR
2
X
n=1
1
J
2
1
(µ
n
)
J
0
µ
n
r
R
J
0
µ
n
ξ
R
exp
2
n
t
R
2
,
G
2
(z, η, t) =
1
2
πat
exp
(z η)
2
4at
exp
(z + η)
2
4at

,
where the µ
n
are positive zeros of the Bessel function, J
0
(µ
n
) = 0. The numerical values
of the first ten µ
n
are specified in Section 3.2.1 (see the first boundary value problem for
0 r R).
Literature: H. S. Carslaw and J. C. Jaeger (1984).
Domain: 0 r R, 0 z < . Second b oundary value problem.
A semiinfinite circular cylinder is considered. The following conditions are prescribed:
w = f (r, z) at t = 0 (initial condition ...
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Publisher Resources

ISBN: 9781466581494