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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
11.2. Fourth-Order One-Dimensional Nonstationary Equations 971
11.2.6 Equations Containing Second Derivative in x and Mixed
Derivatives
1.
2
w
∂t
2
2
w
∂x
2
4
w
∂t
2
∂x
2
= 0.
One-dimensional wave equation with strong dispersion. This equation describes the dy-
namics of interior one-dimensional wave motions in an exponentially stratified fluid as
well as one-dimensional longitudinal vibrations of a rigid Rayleigh bar of constant cross-
section. This is a special case of equation 11.2.6.4 with a(x) = b(x) = c(x) = 1 and
Φ(x, t) = 0.
1
. Particular solutions:
w =
C
1
exp(λt) + C
2
exp(λt)
C
3
exp
λx
1 + λ
2
+ C
4
exp
λx
1 + λ
2

,
w =
C
1
cos(λx) + C
2
sin(λx)
C
3
cos
λt
1 +
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Publisher Resources

ISBN: 9781466581494