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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
1244 SYSTEMS OF LINEAR COUPLED PDES. DECOMPOSITION METHODS
where the function Φ is an arbitrary solution of the equation
(M
1
L + M
1
K
1
σM
2
∆)[Φ] = 0.
3
. Equations (19.1.2.5)–(19.1.2.6) with σ = 0 are invariant under the transformation
u =
e
u + Φ, p = ep + Θ,
where the functions Φ and Θ are arbitrary solutions of the equations
(L + K
1
∆)[Φ] = 0, M
1
[Θ] + M
2
[Φ] = 0.
19.2 First-Order Decompositions. Examples
19.2.1 Systems of Linear PDEs without Mass Forces (f = 0)
Decomposition on the basis of two stream functions.
In the absence of m ass forces (f = 0), it is convenient to set G = 0 in (19.1.2.2) and
(19.1.2.7). In this case, the right-hand side of the ...
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Publisher Resources

ISBN: 9781466581494