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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
11.4. Three- and n-Dimensional Nonstationary Fourth-Order Equations 1001
where
ϕ
nmk
(t) =
2
s
nmk
λ
nmk
Z
t
0
A
nmk
(τ) exp
1
2σ
(t τ)
sin
s
nmk
2σ
(t τ)
if 4νσλ
nmk
1 = s
2
nmk
> 0,
2
s
nmk
λ
nmk
Z
t
0
A
nmk
(τ) exp
1
2σ
(t τ)
sinh
s
nmk
2σ
(t τ)
if 4νσλ
nmk
1 = s
2
nmk
< 0,
1
σλ
nmk
Z
t
0
A
nmk
(τ) exp
1
2σ
(t τ)
(t τ)
if 4νσλ
nmk
1 = 0,
u
nmk
(x) = sin
πnx
a
sin
πmy
b
sin
πkz
c
,
λ
nmk
= π
2
n
2
a
2
+
m
2
b
2
+
k
2
c
2
, A
nmk
(t) =
8
abc
Z
V
f(x, t)u
nmk
(x) dV.
4.

2
∂t
2
c
2
1

2
∂t
2
c
2
2

w = Φ(x, t).
Here x = (x, y, z) and is the three-dimensional Laplace operator. S imilar equations
occur in elasticity theory (see Section 12.6.3).
1
. The general solution of the ...
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Publisher Resources

ISBN: 9781466581494