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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
966 HIGHER-ORDER PAR TIAL DIFFERENTIAL EQUATIONS
Solution of boundary value problems in terms of the Green’s function.
1
. Consider boundary value problems on the interval 0 x l with the general initial
conditions
w = f (x) at t = 0,
t
w = g(x) at t = 0
and various homogeneous boundary conditions. The solution can be represented in terms
of the Green’s function as
w(x, t) =
∂t
Z
l
0
f(ξ)G(x, ξ, t) +
Z
l
0
g(ξ)G(x, ξ, t)
+
Z
t
0
Z
l
0
Φ(ξ, τ )G(x, ξ, t τ) dτ.
(1)
2
. The Green’s functions can be evaluated from the formula
G(x, ξ, t) =
X
n=1
ϕ
n
(x)ϕ
n
(ξ)
kϕ
n
k
2
sin
t
p
a
2
λ
4
n
+ k
p
a
2
λ
4
n
+ k
, (2)
where the λ
n
and ϕ
n
(x) are determined by solving the self-adjoint eigen ...
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Publisher Resources

ISBN: 9781466581494