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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
1148 SECOND-ORDER LINEAR PDES: CLASSIFICATION, PROBLEMS, PARTICULAR SOLUTIONS
TABLE 14.4
Homogeneous linear partial differential equations that admit multiplicative separable solutions
No.
Form of Eq. (14.3.1.1) Form of particular solutions
1
Equation coefficients are
constant
w(x, t) = A exp(λt + β
1
x
1
+ ··· + β
n
x
n
),
λ, β
1
, . . . , β
n
are related by an algebraic equation
2
Equation coefficients are
independent of time t
w(x, t) = e
λt
ψ(x),
λ is an arbitrary constant, x = {x
1
, . . . , x
n
}
3
Equation coefficients are independent
of the coordinates x
1
, . . . , x
n
w(x, t) = exp(β
1
x
1
+ ··· + β
n
x
n
)ψ(t),
β
1
, . . . , β
n
are arbitrary constants
4
Equation coefficients are independent ...
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Publisher Resources

ISBN: 9781466581494