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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
1026 HIGHER-ORDER PARTIAL DIFFERENTIAL EQUATIONS
where p
k
(z) is a polynomial and i
2
= 1. Let r = r(σ) be the number of roots (taking into
account their multiplicities) of the characteristic equation
λ
m
m1
X
k=0
p
k
(σ)λ
k
= 0 (2)
whose real parts are nonpositive (or bounded above) for a given σ. If r is the same (up to a
set of measure zero) for all σ (−∞, ), then E q. (1) is said to be regular with regularity
index r.
Classical equations such as the heat, wave, and L aplace equations are regular.
2
. In the Cauchy problem for a regular equation (1), one should set r initial conditions of
the form
w
t=0
= f
0
(x),
∂w
∂t
t=0
= f
1
(x), . . . ,
r1
w
∂t
r1
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Publisher Resources

ISBN: 9781466581494