Skip to Main Content
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
11.1. Third-Order Partial Differential Equations 951
11.1.4 O n e-Dimensional Equations Containing a Mixed Derivative
and the Second Derivative in t
1.
2
w
∂t
2
a
2
w
∂x
2
b
3
w
∂t∂x
2
= 0.
This equation describes one-dimensional unsteady motions of viscous compressible baro-
tropic fluids.
1
. Particular solutions:
w(x, t) = (A
1
t + A
2
)x
2
+ (B
1
t + B
2
)x +
1
3
aA
1
t
3
+ (aA
2
+ bA
1
)t
2
+ C
1
t + C
2
;
w(x, t) = e
βt
A
1
exp
βx
a +
+ A
2
exp
βx
a +

, a + > 0;
w(x, t) = e
βt
A
1
cos
βx
p
|a + |
+ A
2
sin
βx
p
|a + |

, a + < 0,
where A
n
, B
n
, C
n
, and β are arbitrary constants. The last solution is periodic in x.
2
. Solutions periodic in t:
w(x, t) = e
λx
A cos(ωt µx) + B sin( ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Differential Equations, 2nd Edition

Differential Equations, 2nd Edition

Steven G. Krantz

Publisher Resources

ISBN: 9781466581494