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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
456 SECOND-ORDER PARABOLIC EQUATIONS WITH TWO SPACE VARIABLES
leads to the two-dimensional heat equation
τ
u = a
ξξ
u +
ηη
u
.
See also Niederer (1973) and Boyer (1974).
3.
∂w
∂t
= a

2
w
∂x
2
+
2
w
∂y
2

+

bx
2
+ by
2
k

w, b > 0.
The transformation
w(x, y, t) =
1
cos
2
ab t
exp
b
2
a
tan
2
ab t

x
2
+ y
2
kt
u(ξ, η, τ ),
ξ =
x
cos
2
ab t
, η =
y
cos
2
ab t
, τ =
a
2
b
tan
2
ab t
leads to the two-dimensional heat equation
τ
u =
ξξ
u +
ηη
u.
See also Niederer (1973) and Boyer (1974).
4.
∂w
∂t
=
2
w
∂x
2
+
2
w
∂y
2
+

ax
2
+ by
2

w.
This is a special case of equation 4.3.2.7. Boyer (1976) showed that this equation admits
the separation of variables into 25 systems of coordinates for ...
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Publisher Resources

ISBN: 9781466581494