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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
836 SECOND-ORDER ELLIPTIC EQUATIONS WITH TWO SPACE VARIABLES
where
D
2n
= 2
ce
2n
(0, q)
ce
2n
(0, q)
A
(2n)
0
, D
2n+1
=
1
2
ce
2n+1
(0, q)
ce
2n+1
(0, q)
αB
(2n+1)
1
, q =
1
16
α
2
.
Here, the A
(2n)
0
and B
(2n+1)
1
are the coefficients in the series expansions of the Mathieu
functions; these can be found in M cL achlan (1947).
4
. Consider the second boundary value problem in the upper half-plane (−∞ < x < ,
0 y < ). We assume that a thermal flux is prescribed on the surface of a plate of finite
length and the medium has a constant temperature far away from the plate:
y
w = f (x) for y = 0, |x| < 1,
y
w = 0 for y = 0, |x| > 1,
w w
as x
2
+ y
2
.
The solution of this problem
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Publisher Resources

ISBN: 9781466581494