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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
1074 SYSTEMS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS
Using the Stokes–Helmholtz representation of the displacement vector.
Every solution of Eqs. (1) w ith f = 0 can be represented by the formulas
u = ϕ + curl Ψ, (8)
where Ψ =
1
, Ψ
2
, Ψ
3
) is a solution of the vector wave equation
Ψ
tt
c
2
2
Ψ = 0 (9)
and the function ϕ is a solution of the scalar wave equation (6).
Cauchy–Kovalevskaya solution.
Any solution of Eqs. (1) with f = 0 can be represented in the form
u =
1
[w] + (c
2
1
c
2
2
)div w, (10)
where the vector function w satisfies the equation
2
1
[w] = 0. (11)
Here and in the following, the d’Alembert operators
1
and
2
are given by
1
2
t
c
2
1
,
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Publisher Resources

ISBN: 9781466581494