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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
478 SECOND-ORDER PARABOLIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES
where
G(x, y, z, ξ, η, ζ, t)=
2
l
1
l
2
πat
exp
(zζ)
2
4at

X
n=1
sin
πnx
l
1
sin
πnξ
l
1
exp
π
2
n
2
at
l
2
1

×
1
2
+
X
m=1
cos
πmx
l
2
cos
πmξ
l
2
exp
π
2
m
2
at
l
2
2

.
Domain: 0 x l
1
, 0 y l
2
, 0 z < . First boundary value problem.
A semiinfinite cylindrical domain of a rectangular cross-section is considered. The follow-
ing conditions are prescribed:
w = f (x, y, z) at t = 0 (initial condition),
w = g
1
(y, z, t) at x = 0 (boundary condition),
w = g
2
(y, z, t) at x = l
1
(boundary condition ),
w = g
3
(x, z, t) at y = 0 (boundary condition),
w = g
4
(x, z, t) at y = l
2
(boundary condition ),
w = g
5
(x,
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Publisher Resources

ISBN: 9781466581494