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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
14.2. Basic Problems of Mathematical Physics 1143
For simplicity, here we confine ourselves to the case where the coefficients a
ij
of equations
(14.2.1.1) and (14.2.1.5) have the special form
a
ij
(x, t) = a(x, t)δ
ij
, δ
ij
=
(
1 if i = j,
0 if i 6= j.
This situation is rather frequent in applications; such coefficients are used to describe vari-
ous phenomena (processes) in isotropic media.
First boundary value problem. The function w(x, t) takes prescribed values at the bo-
undary S of the domain:
w(x, t) = g
1
(x, t) for x S. (14.2.2.1)
Second boundary value problem. The derivative along the (outward) normal is pre-
scribed at the boundary S of the domain:
∂w
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Publisher Resources

ISBN: 9781466581494