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Notes by Ben Griffin
1/7
28 (in White) Mathematical Character of the Basic Equations:
Classification of PDE’s
General form:
xx
xy
yy
ABC
D
, where subscript denotes differentiation
(e.g.,
2
xy
xy
)
A, B, …, D are all functions of
,,, ,
yx
but not of the second
derivatives
2
nd
order quasilinear PDE
From this point we can classify a PDE at a point P(x
0
, y
0
), depending on the sign of
the
discriminant
function
2
4
BA
C
this can vary as a function of x, y.
An example of this would be linearized
compressible flow analysis,
22
ˆˆ
2
10
M
.
The Mach number can
vary from subsonic to supersonic in transonic flow.
This vastly changes
the nature of the PDE.
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View Full DocumentNotes by Ben Griffin
2/7
3 Classes
1.
Hyperbolic:
the PDE is hyperbolic at (x
0
, y
0
) if
2
40
BA
C
usually deal with propagation problems, which are characterized by a
second derivative with respect to time.
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 Fall '09
 RENWEIMEI

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