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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
1084 SYSTEMS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS
Incomplete symmetric decomposition of the Stokes equations.
Every solution of system (1)–(2) can also be represented in the symmetric form
u = ϕ + v, p = ϕ
t
+ νϕ + G, (21)
where the vector function v= (v
1
, v
2
, v
3
) satisfies the independent linear nonhomogeneous
equation
v
t
v = f G (22)
and the functions ϕ and v are related by the single equation
ϕ + div v = 0. (23)
Formulas (21) and Eqs. (22) include an arbitrary scalar function G = G(x, t).
By setting v
1
= 0 and G = F in (21)–(23), we obtain an asymmetric representation of
the solutions (18)–(20).
12.7.4 G eneral Solution of the Steady-Stat ...
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Publisher Resources

ISBN: 9781466581494