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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
Chapter 1 8
Duhamel’s Principles.
Some Transformations
18.1 Duhamel’s Principles in Nonstationary Problems
18.1.1 Problems for Homogeneous Linear Equations
Parabolic eq uations with two independent variables.
Consider the problem for the homogeneous linear equation of parabolic type
∂w
∂t
= a(x)
2
w
∂x
2
+ b(x)
∂w
∂x
+ c(x)w (18.1.1.1)
with the homogeneous initial condition
w = 0 at t = 0 (18.1.1.2)
and the boundary conditions
s
1
x
w + k
1
w = g(t) at x = x
1
, (18.1.1.3)
s
2
x
w + k
2
w = 0 at x = x
2
. (18.1.1.4)
By appropriately choosing the values of the coefficients s
1
, s
2
, k
1
, and k
2
in (18.1.1.3)
and (18.1.1.4), one can obtain the first, second, third, and mixed boundary ...
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Publisher Resources

ISBN: 9781466581494