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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
1138 SECOND-ORDER LINEAR PDES: CLASSIFICATION, PROBLEMS, PARTICULAR SOLUTIONS
then k = 0; in this case with a 6= 0, the general solution of the corresponding hyperbolic
equation has the form
w(x, y) = exp(β
1
ξ + β
2
η)
f(ξ) + g(η)
, D = b
2
ac > 0,
ξ = ay
b +
D
x, η = ay
b
D
x,
β
1
=
aq bp
4aD
+
p
4a
D
, β
2
=
aq bp
4aD
p
4a
D
,
where f(ξ) and g(ξ) are arbitrary functions.
3
. In the degenerate case b
2
ac = 0, aq bp = 0 (where the original equation is reduced
to an ordinary differential equation; see the last row in Table 14.1), the general solution of
Eq. (14.1.1.10) is expressed as
w = exp
px
2a

f(ay bx) exp
x
λ
2a
+g(ay bx) exp
x
λ
2a

if λ= p
2
4as > 0
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Publisher Resources

ISBN: 9781466581494