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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
1224 BOUNDARY VALUE PROBLEMS. GREENS FUNCTION
TABLE 17.9
Green’s functions of boundary value problems for equations of various types in bounded
domains. In all problems, the operators L
x
and Γ
x
are the same; x = {x
1
, . . . , x
n
}
Equation
Initial and
boundary conditions
Green’s function
Elliptic equation
L
x
[w] = Φ(x)
Γ
x
[w] = g(x) for x S
(no initial condition required)
G(x, y) =
X
k=1
u
k
(x)u
k
(y)
ku
k
k
2
λ
k
, λ
k
6= 0
Parabolic equation
t
w L
x
[w] = Φ(x, t)
w = f(x) at t = 0
Γ
x
[w] = g(x, t) f or x S
G(x, y, t) =
X
k=1
u
k
(x)u
k
(y)
ku
k
k
2
exp
λ
k
t
Hyperbolic equation
tt
w L
x
[w] = Φ(x, t)
w = f
0
(x) at t = 0
w = f
1
(x) at t = 0
Γ
x
[w] = g(x, t) f or x S
G(x, y, t) =
X
k=1
u
k
(x
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Publisher Resources

ISBN: 9781466581494