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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
1046 HIGHER-ORDER PARTIAL DIFFERENTIAL EQUATIONS
and the general nonhomogeneous boundary conditions
Γ
(1)
m
[w]
n1
X
k=0
b
(1)
mk
(t)
k
w
∂x
k
= g
(1)
m
(t) at x = x
1
(m = 1, . . . , s),
Γ
(2)
m
[w]
n1
X
k=0
b
(2)
mk
(t)
k
w
∂x
k
= g
(2)
m
(t) at x = x
2
(m = s + 1, . . . , n),
(4)
where s 1 and n s + 1. We assume that both sets of the boundary forms Γ
(1)
m
[w]
(m = 1, . . . , s) and Γ
(2)
m
[w] (m = s + 1, . . . , n) are linearly independent, which means that
for any nonzero ψ
m
= ψ
m
(t) the following relations hold:
s
X
m=1
ψ
m
(t
(1)
m
[w] 6≡ 0,
n
X
m=s+1
ψ
m
(t
(2)
m
[w] 6≡ 0.
In what follows, we deal with the nonstationary boundary value problem (1)–(4). It is
assumed that there exist soluti
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Publisher Resources

ISBN: 9781466581494