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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
934 SECOND-ORDER ELLIPTIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES
10.4.2 Equations of the F orm
div [a(x, y, z)w] q(x, y, z)w = Φ(x, y, z)
Equations of this sort are often encountered in heat and mass transfer theory. For brevity,
the equation is written using the notation
div[a(r)w] =
∂x
a(r)
∂w
∂x
+
∂y
a(r)
∂w
∂y
+
∂z
a(r)
∂w
∂z
, r = {x, y, z}.
In what follows, the problems for the equation in question will be considered in a
bounded domain V with a sufficiently smooth surface S. It is assumed that a(r) > 0
and q(r) 0.
First boundary value problem.
The following boundary condition of the first kind is imposed:
w = f (r) for r S.
Solution:
w(
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Publisher Resources

ISBN: 9781466581494