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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
914 SECOND-ORDER ELLIPTIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES
Domain: 0 x a, 0 y x, 0 z c. First boundary value problem.
A right prism whose base is an isosceles right-angled triangle is considered. Boundary
conditions are prescribed:
w = f
1
(y, z) at x = 0, w = f
2
(x, z) at y = 0, w = f
3
(x, z) at y = x,
w = f
4
(x, y) at z = 0, w = f
5
(x, y) at z = c.
Eigenvalues of the homogeneous problem:
λ
nmk
=
π
2
a
2
(n + m)
2
+ m
2
+
π
2
k
2
c
2
; n, m, k = 1, 2, 3, . . .
Eigenfunctions:
w
nmk
=
sin
π
a
(n+m)x
sin
πmy
a
(1)
n
sin
πmx
a
sin
π
a
(n+m)y

sin
πkz
c
.
Domain: 0 x a, 0 y x, 0 z c. Second boundary value problem.
A right prism whose base is an
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Publisher Resources

ISBN: 9781466581494